CAVITATION I N HYDRAULIC STRUCTURES:

O c c u r r e n c e and Prevention

b y

R W P May

R e p o ~ t No SR 7 9 March 1987

Registered Office: Hydraulics Research Limited, Wallingford, Oxfordshire 0x10 8BA. Telephone: 0491 35381. Telex: 848552

This report describes work funded by the Department of the Environment under

Research Contract PECD 7/6/46. It is published on behalf of the Department

of the Environment, but any opinions expressed in this report are not

necessarily those of the funding Department. The work was carried out by

Mr R W P May in Mr J A Perkin's section of the River Engineering Department

of Hydraulics Research, Wallingford, headed by Dr W R White. The nominated

project officers were Dr R P Thorogood for DOE and Dr W R White for HR.

@ Crown copyright 1987

Published by permission of the Controller of Her Majesty's Stationery

Office

A review i s made of l i t e r a t u r e on cav i ta t ion i n large hydraulic s t ruc tures i n order to summarise the present s t a t e of knowledge, provide guidance t o designers, and idencify areas requiring fur ther research. The topics covered include: (1) mechanisms of cavity focaation and collapse; (2 ) cavi ta t ion a t surface i r r egu la r i t i e s , ga te s l o t s , and energy d i ss ipa tors ; (3) cav i ta t ion res is tance of engineering materials; (4) self-aeration and use of aerators f o r preventing cav i ta t ion damage; ( 5 ) modelling of cav i ta t ion and aeration; (6) research needs. The f i r s t par t of the report provides summaries of the avai lable information on each topic. The second part consis ts of a s e r i e s of Appendices which describe i n more d e t a i l the information contained i n over 200 references.

INTRODUCTION

P a g e

1

MECHANISM OF CAVITATION

2.1 D e s c r i p t i o n 2 . 2 C a v i t a t i o n p a f a m e t e r s

OCCURRENCE IN HYDRAULIC STRUCTURES

CAVITATION AT SURFACE IRREGULARITIES

TUNNELS AND GATES

ENERGY DISSIPATORS

MATERIALS

AERATION

8.1 S e l f - a e r a t i o n 8 . 2 A e r a t o r s o n s p i l l w a y s 8 . 3 T u n n e l s

MODELLING

CONCLUSION

ACKNOWLEDGEMENTS

TABLES :

1. P r o p e r t i e s o f p u r e w a t e r 2 . V a l u e s of Ki f o r s u r f a c e i r r e g u l a r i t i e s 3 . Data on p r o t o t y p e a e r a t o r s

FIGURES :

Types o f s u r f a c e i r r e g u l a r i t y C a v f c a t i o n damage c u r v e V a l u e s of K i d f o r s u r f a c e i r r e g u l a r i t i e s V a l u e s o f Ki f o r s u r f a c e i r r e g u l a r i t i e s Types of g a t e s l o t Cavitation p a r a m e t e r s of g a t e s lo t s T y p e s of b a f f l e b l o c k Types of a e r a t o r T y p e s of a i r s u p p l y s y s t e m c o m p a r i s o n o f p r e d i c t e d a i r demands i n t u n n e l s

CONTENTS (CONT'D)

Page

APPENDICES :

A. List of Symbols

B. Cavitation at Surface Irregularities

B.l General 8.2 Theoretical studies 8.3 Laboratory studies R.4 Field studies

C. Tunnels and Gates

C.l Tunnel inlets C.2 Prototype data on gates C.3 Design of gates

D. Energy Dissipators

E. Cavitation Resistance of Materials

E.l Concrete E.2 Metals E.3 Epoxy and polyester resins E.4 Plastics and other materials

F. Air Entrainment

F.l Effect on cavitation F.2 Self-aeration F.3 Aeracors on spillways F.4 Aerators in tunnels

G. Modelling and Instrumentation

G .l Cavitation G.2 Aeration G.3 Instrumentation for aerated flows

H. Future Research

1 INTRODUCTION

The purpose of t h i s l i t e r a t u r e r ev iew is f i r s t l y t o

d e s c r i b e t h e p r e s e n t s t a t e of knowledge abou t t h e

o c c u r r e n c e and p r e v e n t i o n of c a v i t a t i o n i n l a r g e

h y d r a u l i c s t r u c t u r e s , and s e c o n d l y t o i d e n t i f y a r e a s

where f u r t h e r r e s e a r c h i s needed. The s t u d y has been

c a r r i e d o u t as p a r t o f a r e s e a r c h programme funded by

t h e C o n s t r u c t i o n I n d u s t r y D i r e c t o r a t e o f t h e

Department of t h e Environment .

S i n c e t h e s u r v e y i s conce rned w i t h c a v i t a t i o n produced

by t h e f l o w of w a t e r i n high-head s t r u c t u r e s , i t d o e s

n o t c o v e r o t h e r s p e c i a l i s t areas such as pumps and

s h i p p r o p e l l e r s . D e s p i t e t h i s r e s t r i c t i o n , t h e r e

e x i s t s a ve ry l a r g e amount of i n f o r m a t i o n s p r e a d

a c r o s s s e v e r a l d i s c i p l i n e s , and t h e r e f o r e i t is

p o s s t b l e t h a t some s i g n i f i c a n t r e f e r e n c e s may h a v e

b e e n i n a d v e r t e n t l y o m i t t e d . Many u s e f u l s t u d i e s have

been c a r r i e d o u t i n t h e USSR and P R China , and f o r

d e s c r i p t i o n s of t h e s e i t h a s been n e c e s s a r y t o r e l y

ma in ly on p a p e r s p r e s e n t e d at i n t e r n a t i o n a l

c o n f e r e n c e s o r on Eng l i sh - l anguage summaries.

I t i s i n t e n d e d t h a t t h e r e v i e w s h o u l d be of u s e t o

e n g i n e e r s a s w e l l as r e s e a r c h e r s , and i t t h e r e f o r e

c o v e r s a f a i r l y broad f i e l d . S e c t i o n s 2 a n d 3 o f t h e

r e p o r t g i v e a g e n e r a l d e s c r i p t i o n of t h e n a t u r e of

c a v i t a t i o n and of t h e f a c t o r s which govern i ts

o c c u r r e n c e . S e c t i o n s 4 to 9 b r i e f l y summarise t h e

a v a i l a b l e i n f o r m a t i o n on i n d i v i d u a l t o p i c s , and are

l i n k e d t o Appendices B t o G which g i v e more d e t a i l e d

d e s c r i p t i o n s of t h e r e l e v a n t i n f o r m a t i o n i n t h e

r e f e r e n c e s . The f i r s t g r o u p of t o p i c s d e a l s w i t h t h e

main s o u r c e s of c a v i t a t i o n i n h y d r a u l i c s t r u c t u r e s :

s u r E a c e i r r e g u l a r i t i e s i n c h a n n e l s ( S e c t i o n 4 and

Appendix B ) ; t u n n e l i n l e t s and high-head g a t e s

( S e c t i o n 5 and Appendix C ) ; and ene rgy d i s s i p a t o r s

( S e c t i o n 6 and Appendix D ) . The c a v i t a t i o n

r e s i s t a n c e s of eng ineer ing m a t e r i a l s , such a s

conc re t e , s t e e l , r e s i n s and p l a s t i c s , a r e cons ide r ed

i n Sec t ion 7 and Appendix E . S ince t h e presence of

a i r i n water has t h e b e n e f i c i a l e f f e c t of reducing o r

p r even t i ng c a v i t a t i o n damage, Sec t i on 8 and Appendix F

d e s c r i b e in format ion on s e l f - a e r a t i o n and t h e d e s i g n

of a e r a t o r s f o r sp i l lways and tunne ls . Most s t u d i e s

on c a v i t a t i o n and a e r a t i o n have been c a r r i e d o u t in

t h e l a b o r a t o r y , s o t h e problems of s c a l e e f f e c t s i n

modelling a r e d e a l t w i th i n Sec t i on 9 and Appendix G.

F i n a l l y , t o p i c s r e q u i r i n g f u r t h e r r e s e a r c h a r e

i d e n t i f i e d i n Appendix H. Within the Appendices,

r e f e r e n c e s on a p a r t i c u l a r s u b j e c t have normally been

presen ted i n chronolog ica l sequence; a l s o F igu re s a r e

numbered i n t h e o r d e r i n which they a r e r e f e r r e d t o i n

t h e Appendices.

Comparing r e s u l t s and drawing conc lus ions from

d i f f e r e n t , and sometimes c o n f l i c t i n g , s t u d i e s can be

d i f t i c u l t because t he r e a r e u s u a l l y v a r i a t i o n s i n t h e

exper imenta l c o n d i t i o n s , the t echn iques of

measurement, o r the methods of a n a l y s i s . The

summaries i n Sec t i ons 4 t o 9 t h e r e f o r e concen t r a t e on

gene ra l a r e a s of agreement, and f o r more d e t a i l e d

i n fo rma t ion r e a d e r s should r e f e r t o t h e Appendices and

t h e o r i g i n a l r e f e r ences .

2 MRCBANISM OF

CAVITATION

2 .1 Desc r i p t i on

Th i s b r i e f d e s c r i p t i o n of t h e c a v i t a t i o n phenomenon i s

based on in format ion contained i n a comprehensive

textbook by Knapp e t a 1 (1970) and i n surveys produced

by Eisenberg (1961), Johnson (1963). Kenn (1968) and

Knapp (1952) .

A s u i c a b l e d e f i n i t i o n f o r t h e type of cavitation which

w i l l be cons idered i n t h i s r e p o r t was g i v e n by Knapp

(1952) a s " t h e format ion and c o l l a p s e of c a v i t i e s i n a

s t ream of f lowing l i q u i d which r e s u l t s from p r e s s u r e

changes w i t h i n t h e s t r e a m caused by changes i n t h e

v e l o c i t y of flow". T h i s exc ludes c a v i t a t i o n

a s s o c i a t e d wi th t h e v i b r a t i o n of bodies i n s t a t i o n a r y

f l u i d s . Throughout t h i s r e p o r t i t w i l l be assumed

t h a t t h e l i q u i d i n q u e s t i o n i s wate r and t h a t t h e g a s

i s e i t h e r a i r o r water vapour.

The n e g a t i v e p r e s s u r e r e q u i r e d t o form a c a v i t y w i t h i n

pure wa te r i s ex t remely h i g h and c a n be of t h e o r d e r

of s e v e r a l hundred atmospheres. The f a c t t h a t normal

samples of wa te r form c a v i t i e s a t much s m a l l e r

p r e s s u r e s i n d i c a t e s t h a t t h e c a v i t i e s grow from

p r e - e x i s t i n g n u c l e i c o n t a i n i n g e i t h e r wa te r vapour o r

wa te r vapour and a i r . The s i z e s of t h e s e n u c l e i need

t o be i n t h e range 0.1 t o l o p , and two t h e o r i e s have

been proposed t o e x p l a i n t h e i r e x i s t e n c e and

p e r s i s t e n c e . The f i r s t i s t h a t t h e n u c l e i a r e

s t a b i l i z e d w i t h i n t h e i n t e r s t i c e s of mic roscop ic d u s t

p a r t i c l e s ; t h e second is t h a t a n o r g a n i c f i l m forms

around a nucleus and the reby m a i n t a i n s t h e i n t e r n a l

p r e s s u r e and p r e v e n t s d i f f u s i o n of a i r .

When t h e ambient p r e s s u r e i n the l i q u i d f a l l s c lose t o

t h e vapour p r e s s u r e , t h e n u c l e i grow r a p i d l y and

become v i s i b l e a s a c loud of t i n y c a v i t a t i o n b u b b l e s .

The i n c e p t i o n p r e s s u r e which t r i g g e r s t h i s growth i s

u s u a l l y s l i g h t l y lower than t h e vapour p r e s s u r e , h u t

depends upon t h e i n i t i a l s i z e of t h e n u c l e i and upon

t h e r a t i o of a i r p r e s s u r e t o vapour p r e s s u r e w i t h i n

them. The u l t i m a t e s i z e of t h e c a v i t i e s i s determined

by t h e t i m e t h a t they a r e s u b j e c t co p r e s s u r e s lower

t h a n t h e i n c e p t i o n p r e s s u r e .

The main types of c a v i t a t i o n encountered i n c i v i l

e n g i n e e r i n g s i t u a t i o n s a r e :

1. " t r a v e l l i n g c a v i t a t i o n " i n which c a v i t i e s

form i n a r e a s of low p r e s s u r e , t r a v e l wi th

t h e f low and c o l l a p s e i n r e g i o n s of h i g h e r

p r e s s u r e ;

2. " f i x e d c a v i t a t i o n " i n which flow s e p a r a t e s

from a body and forms a q u a s i - s t e a d y c a v i t y

a t t a c h e d t o t h e boundary; when t h e c a v i t y

e x t e n d s beyond t h e g e n e r a t i n g body i t is

r e f e r r e d to as " s u p e r - c a v i t a t i o n " ;

3. " v o r t e x c a v i t a t i o n " i n which c a v i t i e s form

i n t h e c o r e s of f a s t - r o t a t i n g e d d i e s c r e a t e d

i n r e g i o n s of h i g h s h e a r .

When t h e ambient p r e s s u r e i n t h e f l u i d exceeds t h e

vapour p r e s s u r e , c a v i t i e s c o l l a p s e very r a p i d l y and

g e n e r a t e ex t remely h i g h p r e s s u r e s i n t h e i r immediate

v i c i n i t y ; p r e s s u r e s of up t o 15,000 a tmospheres

(1500MPa approx) were measured by L e s l e i g h t e r (1983).

Sound i s a l s o g e n e r a t e d when c a v i t i e s c o l l a p s e and

p rov ides a method of d e t e r m i n i n g t h e o n s e t of

c a v i t a t i o n . I n some s i t u a t i o n s c o l l a p s i n g c a v i t i e s

a r e obse rved t o rebound and go through s e v e r a l c y c l e s

of expans ion and c o n t r a c t i o n . However, when t h e a i r

c o n t e n t i n t h e c a v i t y i s low, t h e bubble c o l l a p s e s

w i t h o u t rebounding.

S o l i d s u r f a c e s a r e damaged by p i t t i n g when c a v i t i e s

c o l l a p s e c l o s e up a g a i n s t them. Measurements of r a t e s

of p i t t i n g i n d i c a t e t h a t o n l y a ve ry small p r o p o r t i o n

of t h e a v a i l a b l e c a v i t i e s are l a r g e enough and

c o l l a p s e c l o s e enough t o a boundary t o cause damage.

During most of t h e i r l i f e t r a v e l l i n g c a v i t i e s appear

t o remain s p h e r i c a l , b u t e x p e r i m e n t a l ev idence

suggests t h a t they may d i s t o r t when co l l aps ing c l o s e

t o boundaries . In these circumstances the wall of t h e

c a v i t y remote from the boundary may fo ld inwards t o

form a needle- l ike j e t of f l u i d . The micro-jet passes

through the cav i ty and emerges a t very high v e l o c i t y

i n t o the f l u i d ad jacent t o t he boundary.

Damage t o s o l i d s u r f a c e s may be caused by the impact

of micro-jets and a l s o by shock waves generated dur ing

the rap id co l l apse of c a v i t i e s . However, exper imenta l

work by Tomita h Shima (1986) ind ica ted t h a t t h e r e i s

a t h i r d and more damaging mechanism, t h a t of

u l t r a - j e t s . These j e t s a r e Formed when shock waves

from a l a r g e r c a v i t y t r i g g e r the very sudden

asymmetric co l l apse of sma l l e r c a v i t i e s . I n the

experiments i t was found t h a t c a v i t a t i o n p i t t i n g was

caused by the u l t r a - j e t s , which produced impact

v e l o c i t i e s of up t o 370rp/s, compared with an average

of 130m/s f o r the l a r g e r micro-jets .

Cav i t a t i on can damage nea r ly a l l m a t e r i a l s i nc lud ing

ve ry s t r o n g ones such as s t a i n l e s s s t e e l . High

pressures generated by c o l l a p s i n g c a v i t i e s cause

mechanical damage t o su r f aces , and with chemically

i n e r t s o l i d s and l i q u i d s t h i s i s probably the only

mechanism involved. However, i n t he ca se of meta ls

t h e damage is acce l e ra t ed by chemical and

e lec t rochemica l e f f e c t s , perhaps because p r o t e c t i v e

oxide l a y e r s a r e con t inua l ly being removed by t h e

mechanical a c t l o n of the c a v i t a t i o n . No s i n g l e

mechanical o r chemical proper ty ( f o r i n s t ance

d u c t i l i t y o r hardness) has been found t o c o r r e l a t e t he

r e l a t i v e r e s i s t a n c e 6 of d i f f e r e n t m a t e r i a l s t o

c a v i t a t i o n a t t a c k .

This r e s i s t a n c e i s o f t e n measured i n terms of the r a t e

of l o s s of Inass per u n i t a rea . For d u c t i l e m a t e r i a l s

t h e l o s s r a t e tends t o vary cons ide r ab ly with time.

During an i n i t i a l " incuba t ion" per iod t h e mechanical

a t t a c k produces work-hardening of the s u r f a c e but

l i t t l e l o s s of weight ; beyond t h e i ncuba t i on per iod

t h e l o s s r a t e i n c r e a s e s cons iderab ly . By c o n t r a s t ,

more b r i t t l e m a t e r i a l s do not e x h i b i t an i ncuba t i on

p e r i o d , but l o s e mass a t a s t e a d i e r speed. I n t h e

c a s e of conc re t e , c a v i t a t i o n a t t a c k s t h e weaker mor ta r

u n t i l t h e agg rega t e is undermined and then removed.

For t h e s e reasons i t is necessa ry t o t a k e account of

t h e du ra t i on of a t t a c k when cons ide r i ng the r e l a t i v e

r e s i s t a n c e of d i f f e r e n t m a t e r i a l s .

The r a t e of damage f o r a g iven m a t e r i a l c l e a r l y a l s o

depends upon t h e i n t e n s i t y o f the c a v i t a t i o n . I f , f o r

example, t h e ambient p r e s s u r e i n a t e s t is g r a d u a l l y

decreased , a p o i n t of " i n c i p i e n t " c a v i t a t i o n w i l l be

reached a t which t i n y bubbles f i r s t become v i s i b l e ;

a l t e r n a t i v e l y t h i s l i m i t is sometimes de f i ned by t h e

s t a r t of c a v i t a t i o n no i s e o r by a sudden change i n t h e

tu rbu lence c h a r a c t e r i s t i c s of t h e flow. Measurements

show t h a t t h e r a t e of m a t e r i a l loss i s n e g l i g i b l e a t

t h e p o i n t of i n c i p i e n t c a v i t a t i o n , i n c r e a s e s t o a peak

a t a h ighe r s t a g e of c a v i t a t i o n , and then dec r ea se s

aga in . D i f f e r e n t m a t e r i a l s may reach t h e i r peak

e r o s i o n r a t e s a t d i f f e r e n t i n t e n s i t i e s of c a v i t a t i o n

s o t h a t comparative t e s t s m y be misleading i f they

a r e not c a r r i e d o u t under equ iva l en t p ro to type

c o n d i t i o n s . The occur rence of c a v i t a t i o n a l s o

e x h i b i t s a h y s t e r e s i s e f f e c t wi th vary ing ambient

p r e s s u r e ( o r v e l o c i t y ) . With a dec r ea s ing p r e s s u r e

t h e c a v i t a t i o n begins a t a lower p r e s su re than the one

a t which i t cea se s when t h e p r e s su re is increased .

The term " i n c i p i e n t " is a p p l i e d t o the l i m i t of

c a v i t a t i o n i f t h e c a v i t a t i o n i s s t a r t i n g , and

"de s inen t " i f i t is ending.

Injecting air into water cushions the pressures

generated by collapsing cavities, and can

significantly reduce or eliminate the amount of

damage. Cathodic or anodic protection of metals in

water is effective in reducing cavitation erosion;

gas (hydrogen or oxygen) released at the surface

cushions the collapse of the cavities in a similar way

to injected air.

Techniques for measuring the cavitation resistance of

materials include:

1. Venturi tubes - cavities are generated in the throat and a sample is placed downstream

at the point where they collapse;

2. Water tunnels - samples are placed downstream of a cylindrical body which

produces cavities in its wake;

3. Vibrating equipment - application of an oscillating electromagnetic field to a

suitable metal or crystal produces small

amplitude extensions and contractions; this

magnetostrictive principle is used to

produce cavitation on samples by vibrating

them at high frequency (typically 5-20kHz)

in a stationary liquid. An alternative

technique uses ultrasonic vibrations of a

liquid to cause cavitation on a stationary

sample;

4. Drop-impact equipment - samples are attached to a disc which is rotated at high speed

through a jet of liquid. Although the

method does not produce cavitation, the

resulting erosion is quite similar in

nature; this lends support to the theory

t h a t c a v i t a t i o n damage i s caused by

high-speed j e t s of l i q u i d ( s e e above) .

S ince t e c h n i q u e s 1 and 2 use f lowing wa te r , t h e y

s h o u l d reproduce c a v i t a t i n g c o n d i t i o n s i n h y d r a u l i c

s t r u c t u r e s more c l o s e l y t h a n 3 and 4. However,

r e s u l t s from 1 and 2 a r e s u s c e p t i b l e t o changes i n

wa te r t e m p e r a t u r e , a i r c o n t e n t and d u s t c o n t e n t .

Machines u s i n g t e c h n i q u e s 3 o r 4 a r e cheaper t o b u i l d

and s i m p l e r t o o p e r a t e , and method 4 i s l e s s s e n s i t i v e

t o v a r i a t i o n s i n t h e p r o p e r t i e s of t h e wa te r . None of

t h e s e t e c h n i q u e s c a n be expec ted t o p r e d i c t t h e

p r e c i s e behav iour of a m a t e r i a l i n a p r o t o t y p e

s i t u a t i o n ; however, they can be used t o r a n k

m a t e r i a l s i n terms of t h e i r r e l a t i v e r e s i s t a n c e t o

c a v i t a t i o n . I n g e n e r a l t h e f o u r methods produce

s i m i l a r r a n k i n g s , bu t some i n c o n s i s t e n c i e s do a r i s e ,

even between machines u s i n g t h e same t echn ique . Knapp

e t a 1 (1970, T a b l e s 9 . 1 t o 9.14) g i v e comprehensive

d a t a f o r a wide range of m e t a l s and a l l o y s .

2 . 2 C a v i t a t i o n

p a r a m e t e r s

Cons ide r t h e c o n d i t i o n s r e q u i r e d t o produce c a v i t a t i o n

a t a p a r t i c u l a r p o i n t i n a f low ( e g a t a s t e p i n t h e

boundary o r a t an o b s t r u c t i o n ) . L e t p. be t h e

t ime-averaged a b s o l u t e s t a t i c p r e s s u r e and V t h e 0

t ime-averaged v e l o c i t y a t a reEerence p o i n t 0 i n t h e

u n d i s t u r b e d f low. The i n s t a n t a n e o u s s t a t i c p r e s s u r e

p l a t t h e p o i n t of i n t e r e s t i s found from B e r n o u l l i ' s

e q u a t i o n t o b e

where p i s t h e d e n s i t y of t h e f l u i d , g i s t h e

a c c e l e r a t i o n due t o g r a v i t y and z i s t h e e l e v a t i o n of

p o i n t 1 above t h e r e f e r e n c e p o i n t 0. (A f u l l l i s t of

symbols i s g i v e n i n Appendix A). The f a c t o r 6 i s t h e

p r o p o r t i o n a t e change i n t h e t ime-averaged v e l o c i t y

caused by t h e o b s t r u c t i o n o r change i n boundary shape.

The f a c t o r E d e s c r i b e s t h e i n s t a n t a n e o u s f l u c t u a t i o n

i n v e l o c i t y due t o t h e g e n e r a l t u r b u l e n c e i n t h e f low

and any a d d i t i o n a l f l u c t u a t i o n s produced by t h e change

i n boundary shape o r by e d d i e s . I f t h e a b s o l u t e

p r e s s u r e p l f a l l s below a c r i t i c a l v a l u e p n u c l e i C'

a l r e a d y e x i s t i n g i n t h e f low w i l l expand r a p i d l y t o

form c a v i t i e s .

An i m p o r t a n t r equ i rement f o r dynamic s i m i l a r i t y

between d i f f e r e n t tests i s t h e c a v i t a t i o n index of t h e

f low d e f i n e d by

where p i s t h e vapour p r e s s u r e of t h e l i q u i d a t t h e v

t e s t t empera tu re . I n c i p i e n t c a v i t a t i o n o c c u r s when

t h e l o c a l p r e s s u r e p l d rops t o t h e c r i t i c a l p r e s s u r e

pc. The c o r r e s p o n d i n g v a l u e of t h e c a v i t a t i o n i n d e x ,

d e f i n e d i n terms of t h e mean f low c o n d i t i o n s a t t h e

r e f e r e n c e p o s i t i o n , i s

which shows t h a t c a v i t a t i o n may be i n i t i a t e d by

d e c r e a s i n g p o r i n c r e a s i n g V . From Equa t ions l and 0 0

3 i t f o l l o w s t h a t

I t can be s e e n t h a t K may n o t n e c e s s a r i l y remain i

c o n s t a n t f o r a p a r t i c u l a r f l o w geometry. The c r i t i c a l

p r e s s u r e p i s u s u a l l y s l i g h t l y lower than p b u t C v

v a r i e s a c c o r d i n g t o t h e s i z e and number of n u c l e i t h a t

t h e l i q u i d c o n t a i n s ( s e e 2 .1) . The f a c t o r 6 i s a

f u n c t i o n of t h e boundary geometry , and may a l s o depend

upon t h e Reynolds number of t h e f low. The f a c t o r E

v a r i e s w i t h t h e t u r b u l e n c e l e v e l of t h e f l u i d and t h e

i n t e n s i t y of e d d i e s g e n e r a t e d i n s h e a r zones . These

d i f f e r e n c e s s e r v e t o e x p l a i n why measured v a l u e s of K i

do n o t a lways a g r e e between model and p r o t o t y p e o r

between one model and a n o t h e r .

When comparing d i f f e r e n t t e s t r e s u l t s i t i s n e c e s s a r y

t o e n s u r e t h a t t h e c a v i t a t i o n p a r a m e t e r s have been

d e f i n e d i n t h e same way. The c a v i t a t i o n i n d e x is more

c o r r e c t l y d e f i n e d w i t h p i n E q u a t i o n 2 r e p l a c e d by 0

(po - g z ) , b u t t h i s a l t e r n a t i v e d e f i n i t i o n i s l e s s

common, p a r t l y because t h e p o i n t of c a v i t y f o r m a t i o n

c a n v a r y o r may n o t be known p r e c i s e l y . The r e f e r e n c e

p o s i t i o n 0 might be chosen ups t ream of t h e p o i n t of

i n t e r e s t , a s i n t h e c a s e of a n upward s t e p i n t h e

f l o o r of a channe l . However, i n t h e c a s e of a n

o r i f i c e t h e r e f e r e n c e p o i n t might be chosen downstream

i n t h e vena c o n t r a c t a . The r e f e r e n c e v e l o c i t y V i s 0

sometimes t a k e n t o be t h e depth-averaged v e l o c i t y and

sometimes t h e u n d i s t u r b e d l o c a l v e l o c i t y c l o s e t o t h e

p o i n t of i n t e r e s t .

The i n t e n s i t y of c a v i t a t i o n can b e d e s c r i b e d i n t e r m s

of t h e pa ramete r I g i v e n by:

C a v i t a t i o n damage does n o t o c c u r i f I < 0, and f o r a

g i v e n m a t e r i a l r e a c h e s a maximum r a t e a t a v a l u e of

I between 0 and 1. m

I n o r d e r t o c a l c u l a t e v a l u e s of t h e c a v i t a t i o n

p a r a m e t e r K , i t i s n e c e s s a r y t o t a k e accoun t of any

variation of atmospheric pressure with alcitude and

also the strong dependence of the vapour pressure of

water, pv, on temperature; values of p (from v

Batchelor, 1967) are given in Table 1.

3 OCCURRENCE IN

HYDRAULIC

STRUCTURES

In most hydraulic structures the ambient pressure is

close to atmospheric, so cavitation is normally

associated with flows of high velocity. Cavitation

problems can arise when the velocity reaches about

15m/s, and above 25mfs serious damage can be expected

if adequate precautions are not taken. Structures

where damage has been reported include:

1. open-channel spillways

2. bottom outlets in dams

3. high-head gates and gate slots

4. energy dissipators including hydraulic-jump

stilling basins.

Cavitation can also occur in pumps, valves and in

pipelines under surge conditions, but these instances

are outside the scope of this review.

If a flow remains attached to a bounding surface,

cavitation-producing pressures are normally the result

of turbulent velocity fluctuations in the boundary

layer andfor of flow curvature. The point of minimum

pressure on a surface can be measured or can

sometimes be calculated theoretically from potential

theory, with if necessary a suitable allowance for the

displacement thickness of the boundary layer.

However, turbulent fluctuations may cause cavitation

to occur sooner than predicted, while the position at

which it starts may be downstream of the point of

minimum pressure (due for example to the formation of

a l aminar s e p a r a t i o n bubble) . I f a p r e s s u r e

t r a n s d u c e r , mounted a t a s u i t a b l e p o i n t on t h e

boundary, i n d i c a t e s t r a n s i e n t v a l u e s c l o s e t o vapour

p r e s s u r e , then c a v i t a t i o n i s l i k e l y t o occur . Damage

w i l l normal ly t a k e p l a c e c l o s e t o t h e s p o t a t which

t h e c a v i t i e s a r e g e n e r a t e d .

I f a f low s e p a r a t e s from a s u r f a c e , c a v i t i e s w i l l f o rm

f i r s t i n t h e f a s t - r o t a t i n g e d d i e s t h a t a r e shed

downstream. The p r e s s u r e i n t h e e d d i e s w i l l be lower

t h a n a t t h e p o i n t of s e p a r a t i o n , s o surface-mounted

t r a n s d u c e r s w i l l n o t p r o v i d e a good i n d i c a t i o n of t h e

l i k e l i h o o d of c a v i t a t i o n . The c a v i t i e s w i l l be swept

downstream and w i l l c o l l a p s e when they e n t e r a r e g i o n

o f h igh p r e s s u r e . Damage caused by s h e a r f l o w s can

t h e r e f o r e occur a c o n s i d e r a b l e d i s t a n c e downstream of

t h e p o i n t of s e p a r a t i o n . T h i s type of c a v i t a t i o n can

be produced by l o c a l i r r e g u l a r i t i e s i n t h e boundary

(e .g . s h a r p s t e p s a t j o i n t s ) o r by t h e o v e r a l l

geometry of t h e s t r u c t u r e . Examples of t h e l a t t e r

i n c l u d e h o r i z o n t a l s h e a r f lows g e n e r a t e d by

h i g h - v e l o c i t y submerged jets, o r v e r t i c a l s h e a r f l o w s

c r e a t e d by a sudden i n c r e a s e i n channe l wid th (e.g.

two o r more c o n t r o l g a t e s d i s c h a r g i n g t o a s i n g l e

t u n n e l ) .

4 SURFACE

IRREGULARITIES

The p r i n c i p a l method of p r e d i c t i n g whether a s u r f a c e

i r r e g u l a r i t y w i l l c a u s e c a v i t a t i o n i n a p r o t o t y p e

s t r u c t u r e i s t o c a l c u l a t e t h e c a v i t a t i o n number K of

t h e f low from Equa t ion 2 , and compare i t w i t h

p r e v i o u s l y determined v a l u e s of t h e i n c i p i e n t

c a v i t a t i o n i n d e x K f o r t h a t type of i r r e g u l a r i t y ; i

c a v i t a t i o n w i l l occur i f K < K i'

Values of K have been o b t a i n e d f o r many t y p e s of i i r r e g u l a r i t y , some of which a r e shown i n F i g u r e 1.

The methods of determining K include: i

1. theoretical predictions of the minimum

pressure on the surface of the

irregularity;

2. laboratory measurements of the minimum

pressure on the surface of the

irregularity;

3. laboratory observations of cavity formation

using cavitation tunnels (no free surface)

or vacuum test rigs (with free surface);

4. field measurements of surface pressure or

cavitation damage at irregularities.

Results based on field studies are the most

appropriate, but very few are available because of the

difficulties of carrying out controlled tests. If the

flow separates at an irregularity, the lowest

pressures will occur in eddies within the fluid;

values of K. determined from measured or predicted 1

surface pressures may thus be under-estimated. Data

from cavitation tunnels and vacuum test rigs, backed

up by field measurements, should therefore be used

where possible.

In general, most of the experimental results for a

given type of irregularity are in reasonable

agreement. Discrepancies between tests do exist, but

they are normally fairly small in comparison with the

effects produced by minor changes in shape (e.g.

rounded edges instead of sharp edges). Moreover,

irregularities due to construction faults in spillways

and tunnels have three-dimensional shapes which will

seldom match precisely those tested in the

laboratory.

Movement of c o n c r e t e formwork i s t h e most common cause

of i r r e g u l a r i t i e s , and can g i v e r i s e t o a b r u p t o f f s e t s

and chamfers ( b o t h i n t o and away from t h e f l o w ) ,

sudden changes i n s l o p e , cusped j o i n t s , and

u n d u l a t i o n s ( s e e Types 1, 2, 3, 4 , 5 , 6 and 7D i n

F i g u r e 1 ) . Of t h e s e , a b r u p t o f f s e t s i n t o t h e f low

(Type 1A) have t h e g r e a t e s t c a v i t a t i o n p o t e n t i a l , and

a s u i t a b l e formula f o r c a l c u l a t i n g t h e K va lue i s i

t h a t due t o L i u (1983) ,

where h is t h e h e i g h t of t h e s t e p i n mm. T h i s

e q u a t i o n g i v e s v a l u e s which a r e i n r e a s o n a b l e

agreement wi th t h e d a t a of B a l l (1963), and somewhat

h i g h e r than t h o s e g i v e n by Falvey (1982) and Scheur

(1985); s e e S e c t i o n B.3 i n Appendix B. I f t h e edge

of t h e o f f s e t i s rounded t o a r a d i u s of r = 0.5h, t h e

v a l u e of K i s reduced t o 86% of t h a t g iven by i

Equa t ion 6. When c a l c u l a t i n g t h e c a v i t a t i o n number K

of t h e f low from Equa t ion 2, the v a l u e s of v e l o c i t y

V and a b s o l u t e s t a t i c p r e s s u r e p should be those a t 0 0

t h e l e v e l of t h e t o p of t h e o f f s e t ; f o r a

fu l ly -deve loped boundary l a y e r V can be de te rmined 0

from Equat ion B.26. S u r f a c e i r r e g u l a r i t i e s j u s t

downstream of high-head g a t e s a r e p a r t i c u l a r l y l i a b l e

t o cause c a v i t a t i o n because t h e boundary l a y e r s a r e

ve ry t h i n , and do not p r o t e c t t h e i r r e g u l a r i t i e s from

t h e h i g h f r e e - s t r e a m v e l o c i t i e s .

The c a v i t a t i o n p o t e n t i a l of c o n s t r u c t i o n f a u l t s can be

reduced by g r i n d i n g them t o form chamfers. For an

in to - f low chamfer (Type 3A), t h e s lope needed t o lower

t h e va lue of K below t h e c a v i t a t i o n number K of t h e i f l o w can be e s t i m a t e d from t h e f o l l o w i n g e m p i r i c a l

e q u a t i o n s o b t a i n e d by Novikova & Semenkov (1985)

Ki = 2.3 , f o r n S 1 ( 7 )

K. = 2.3n-0.7 , f o r n > 1 1 ( 8 )

where t h e s l o p e i s n u n i t s p a r a l l e l t o t h e f low t o o n e

u n i t normal t o t h e f low. These e q u a t i o n s g i v e

somewhat h i g h e r v a l u e s of K t h a n most of t h e o t h e r i

l a b o r a t o r y s t u d i e s d e s c r i b e d i n S e c t i o n 8 .3 o f

Appendix B.

Data f o r chamfers ang led away from t h e f low (Types & A .

B) a r e l i m i t e d , and may no t be comparable because of

d i f f e r e n t d e f i n i t i o n s of t h e c h a r a c t e r i s t i c v e l o c i t y

( e .g . n e a r t h e bed, o r depth-averaged) . Labora to ry

s t u d i e s i n d i c a t e t h a t t h e v a l u e s of K i t end t o be

lower than f o r in to - f low chamfers of e q u a l s l o p e .

A s t h e f low v e l o c i t y is i n c r e a s e d , t h e s t a n d a r d s of

s u r f a c e f i n i s h r e q u i r e d t o p r e v e n t c a v i t a t i o n

e v e n t u a l l y become i m p r a c t i c a b l e , p a r t i c u l a r l y i n c a s e s

where a convex s u r f a c e reduces t h e s t a t i c p r e s s u r e , o r

t h e boundary l a y e r s a r e no t f u l l y developed. Some

r e f e r e n c e s s u g g e s t t h a t u s e of t h e parameter K f o r i

c a v i t a t i o n i n c e p t i o n i s n o t a p p r o p r i a t e i n d e s i g n ,

because damage does n o t occur u n t i l t h e c a v i t a t i o n

i n d e x K of t h e f low f a l l s below K . Wang h Chou i

(1979) proposed t h a t t h e d e s i g n c r i t e r i o n shou ld be K

b 0 . 8 K . F i e l d t e s t s a t B r a t s k Dam (USSR) r e p o r t e d i

by G a l p e r i n e t a 1 (1977) and Oskolkov h Semenkov

(1979) p rov ided v a l u e s of t h e i n d e x K f o r i n c i p i e n t i d

damage a t chamfers ang led i n t o and away from t h e f l o w .

The r e s u l t s a r e p r e s e n t e d i n F i g u r e 3 , and i n d i c a t e

t h a t chamfers away from t h e f low have s l i g h t l y h i g h e r

v a l u e s of K t h a n chamfers p r o j e c t i n g i n t o t h e f low. i d

Comparison w i t h E q u a t i o n s 7 and 8 a l s o shows t h a t t h e

f i e l d measurements of K a r e l a r g e r than t h e i d

l a b o r a t o r y v a l u e s of K f o r s l o p e s of n > 8; t h i s i

a p p a r e n t d i s c r e p a n c y may be due t o d i f f e r e n t

d e f i n i t i o n s of t h e c h a r a c t e r i s t i c v e l o c i t y used when

c a l c u l a t i n g t h e c a v i t a t i o n index .

Information about the cavitation characteristics of

other types of surface irregularity is provided in

Appendix B.

Another factor to be considered in design is the

likely duration of the cavitation attack; as the

cavitation number K of the flow decreases, the safe

operating time is reduced. Falvey (1983) used field

data to produce Figure 2, which shows a relationship

between the value of K, its duration and the amount of

cavitation damage.

5 TLINNELS AND GATES

Cavitation can be a potentially serious problem in

intermediate and low-level outlets in dams, and may

occur at inlets to tunnels, at high-head gates, and in

tunnels downstream of gates.

Convergence and curvature of the flow entering a

tunnel can produce sub-atmospheric pressures, which

together with the effect of turbulent fluctuations may

be low enough to cause cavitation. Section C.1 in

Appendix C describes some studies which give

information on pressures along the boundaries of

circular and elliptical entrances. However, if the

flow separates in an inlet, such methods will

under-estimate the likelihood of cavitation, because

the lowest pressures will not occur at the boundaries

but within the fluid. Separation may be caused by a

poorly-designed transition, by a notch or slot, or by

a secondary flow issuing from a connecting shaft.

The supports and lifting mechanisms for vertical leaf

gates are normally located on the downstream side of

the gate, and are accommodated in slots in the side

walls so as to protect them from high velocity flow.

Such slots have often been a cause of cavitation

damage. High v e l o c i t y f low p a s t a r e c t a n g u l a r s l o t

may produce c a v i t a t i o n i n t h r e e ways:

1. flow s e p a r a t i o n a t t h e upst ream c o r n e r , w i t h

c a v i t i e s being g e n e r a t e d i n t h e f r e e s h e a r

l a y e r and c a r r i e d downstream by t h e f low;

2. f low s e p a r a t i o n a t t h e downstream c o r n e r ,

w i t h c a v i t i e s c o l l a p s i n g where t h e f low

r e - a t t a c h e s t o t h e w a l l of t h e t u n n e l ;

3. v o r t e x f o r m a t i o n w i t h i n t h e s l o t , w i t h

p o s s i b l e damage t o t h e s i d e s and t h e g a t e

s u p p o r t s .

The r e l a t i v e importance of t h e s e s o u r c e s v a r i e s w i t h

t h e a s p e c t r a t i o of t h e s l o t , and may be a l t e r e d by

t h e use of o f f s e t s and t r a n s i t i o n s .

Many s t u d i e s have been made of two-dimensional f l o w

p a s t v a r i o u s shapes of s l o t , some of which a r e shown

i n F i g u r e 5. The tests cor respond approx imate ly t o

t h e c o n d i t i o n s which e x i s t when a g a t e is f u l l y open

and t h e s l o t i s no t occupied by t h e l i f t i n g mechanism.

Some s t u d i e s have compared d i f f e r e n t shapes of s l o t on

t h e b a s i s of p r e s s u r e measurements around t h e

boundar ies . However, s t u d i e s c a r r i e d o u t i n

c a v i t a t i o n t u n n e l s a r e more u s e f u l and r e l i a b l e ,

because t h e c o n d i t i o n s f o r c a v i t a t i o n i n c e p t i o n can be

measured d i r e c t l y .

There i s g e n e r a l agreement between s t u d i e s abou t which

t y p e s of g a t e s l o t have t h e lowes t c a v i t a t i o n

p o t e n t i a l . A p l a i n r e c t a n g u l a r s l o t (Type 1 A i n

F i g u r e 5 ) i s s a t i s f a c t o r y f o r low heads , b u t J i n e t a 1

(1980) recommend t h a t t h e l e n g t h f d e p t h r a t i o shou ld be

k e p t i n t h e range 1.4 < Lfh < 2.5, and i f p o s s i b l e

between 1.6 4 L f h 4 1.8 f o r t h e b e s t performance.

Strong vortex action occurs if L/h < 1.2, and

cavitation due to flow separation becomes serious if

L/h > 2.5. Offsetting the wall downstream of the slot

(as in Type 1B) is, by itself, not effective; the

offset reduces the risk of cavitation at the

downstream corner of the slot, but increases it at the

upstream one. The designs which were found to have

the lowest cavitation potential were slots with an

offset (t/h 0.2) and either a radiused transition

(Type 4 B , 100 < r/t < 250) or an elliptical transition

(Type SA, E/t = 5).

Information on values of the incipient cavitation

parameter K. for gate slots of Type 1A and 1B are 1

given by Galperin et a1 (1977). Separate values of K i are calculated for the upstream and downstream corners

of the slot, and take account of the width of the

conduit, the aspect ratio of the slot, the amount of

any downstream offset, and the relative thickness of

the boundary layer. The method of determining K. 1

using Equation C.l and Figure 6 is described in

Section C.3 of Appendix C.

The results of Galperin et a1 are in reasonable

agreement with the following empirical equation which

Jin et a1 (1980) obtained for a plain rectangular slot

(Type 1A):

Kir = 0.38 (~/h) , for 1.5 S L/h S 3.5 (9)

The cavitation index is defined in terms of the

average velocity and pressure just upstream of the

slot, and its value relates to the slot as a whole

(not to the upstream and downstream corners

separately). The cavitation index K for a Type 3D i

slot was found to be related to Kir for a rectangular

slot of the same aspect ratio by the relation:

T h i s r e s u l t was o b t a i n e d f o r a t r a n s i t i o n s l o p e of n =

1 2 , and i t was recommended t h a t t h e r a d i u s should be

approx imate ly r = O.lh, and t h e o f f s e t of t h e

downstream c o r n e r should be i n t h e range 0.05 ,< t / L S

0.08. Equat ion 10 can a l s o be used t o e s t i m a t e K f o r i

s l o t s of Type 3B ( w i t h n = 1 2 ) o r 4A by p u t t i n g e i t h e r

r = O o r t = O .

Although s l o t s of Type 4B and SA a r e recommended,

i n f o r m a t i o n on t h e i r K v a l u e s i s l i m i t e d . Rosanov e t i

a 1 (1965) gave s e p a r a t e v a l u e s of K f o r t h e ups t ream i

and downstream c o r n e r s of s l o t s , and found t h a t K was i

less than 0 .3 f o r an e l l i p t i c t r a n s i t i o n (Type 5A) o f

l e n g t h E = L.

The r e s u l t s d e s c r i b e d above a r e f o r empty s l o t s , b u t

t h e p r e s e n c e of a g a t e r a i l c a n a l t e r t h e f low

c o n d i t i o n s a t t h e downstream c o r n e r . I f a g a t e r a i l

p r o j e c t s i n t o t h e s l o t , t h e n o t c h between t h e edge of

t h e r a i l and t h e downstream f a c e of t h e s l o t shou ld be

£ a i r e d i n o r d e r t o p r e v e n t f l o w s e p a r a t i o n .

When a l e a f g a t e i s p a r t i a l l y open, t h e f low p a s t t h e

s l o t becomes th ree -d imens iona l , and i s i n f l u e n c e d by

t h e shape and p rox imi ty of t h e g a t e . The i n c i p i e n t

c a v i t a t i o n number K . of a g a t e is h i g h e r i f i t is 1

submerged on t h e downstream s i d e than i f i t d i s c h a r g e s

f r e e l y . Above t h e l e v e l of t h e g a t e l i p , t h e l i f t i n g

mechanism s h o u l d , i f p o s s i b l e , f u l l y occupy t h e s l o t .

I f i t does n o t , downward f low d e v e l o p s i n t h e s l o t ;

t h i s i n c r e a s e s t h e v a l u e of K and can r e s u l t i n i '

a d d i t i o n a l c a v i t a t i o n damage on t h e w a l l nea r t h e

f l o o r of t h e t u n n e l .

Gate lips should be designed to produce a clean flow

separation without re-attachment. A lip with a smooth

upstream profile produces less intense separation

under submerged conditions, and reduces the risk of

cavities forming in the horizontal shear layer between

the high-velocity jet and the water above it.

Cavitation in such shear layers can cause serious

damage along walls downstream of partially-open

gates.

Radial gates with attached seals have the advantage of

not requiring slots. Under submerged conditions,

cavitation occurs along the bottom edge of the gate,

and is particularly intense at the side walls.

Alternatively, radial gates may close against recessed

seals mounted in offsets in the walls and floor of the

tunnel. The values of K. for the offsets are similar 1

to those for the upstream corners of gate slots.

High-velocity flow through small gaps and at gate

seals can lead to cavitation damage. Seals should

have smooth profiles in order to prevent flow

separation. Gaps of more than 2mm can result in

serious erosion, and the seals may themselves be

damaged by vibrations induced by unstable cavity

formation.

Information on the cavitation characteristics of gates

tends to be specific, and model tests may be needed to

investigate a particular arrangement. Galperin et a1

(1977) give results of several studies, details of

which are summarised in Section C.3 of Appendix C.

6 ENERGY DISSIPATORS

Most t y p e s of energy d i s s i p a t o r produce l a r g e amounts

of f low t u r b u l e n c e . C a v i t a t i o n w i l l occur i f t h e

v e l o c i t y f l u c t u a t i o n s a r e l a r g e enough t o c a u s e t h e

s t a t i c p r e s s u r e t o f a l l o c c a s i o n a l l y t o t h e vapour

p r e s s u r e of t h e wa te r .

L a b o r a t o r y and p r o t o t y p e measurements of p r e s s u r e s

benea th h y d r a u l i c jumps i n d i c a t e t h a t t h e maximum

r o o t mean-square ( rms) v a l u e s of t h e f l u c t u a t i o n s a r e

t y p i c a l l y between 3% and 9% of t h e v e l o c i t y head

e n t e r i n g t h e jump. Using a s i l l t o produce a f o r c e d

jump s h o r t e n s t h e d i s t a n c e o v e r which t h e energy

d i s s i p a t i o n o c c u r s , and t e n d s , a s might be expec ted .

t o i n c r e a s e t h e magnitude of t h e rms f l u c t u a t i o n s on

t h e f l o o r of t h e b a s i n . Flow s e p a r a t i o n behind b a f f l e

b locks and c h u t e b l o c k s can produce much l a r g e r

v a r i a t i o n s i n p r e s s u r e ; f o r example, Lopardo e t a 1

(1982) measured r m s f l u c t u a t i o n s on t h e r e a r f a c e of a

c h u t e b l o c k e q u a l t o 271 of t h e upst ream v e l o c i t y

head.

Near t h e t o e of a jump, t h e p o s i t i v e p r e s s u r e

f l u c t u a t i o n s t e n d t o be l a r g e r t h a n t h e n e g a t i v e o n e s ,

b u t f u r t h e r downstream t h e d e p a r t u r e s from t h e mean

become more symmet r i ca l and conform approx imate ly t o a

Gauss ian p r o b a b i l i t y d i s t r i b u t i o n . Bowever, i n zones

of f low s e p a r a t i o n , t h e n e g a t i v e f l u c t u a t i o n s may

become b i g g e r than t h e p o s i t i v e ones . Thus, f o r a

g i v e n r m s l e v e l of t u r b u l e n c e , c a v i t a t i o n i s more

l i k e l y behind a s i l l o r b a f f l e b lock t h a n on a l e v e l

f l o o r .

Lopardo e t a 1 (1985) compared model and p r o t o t y p e

d a t a , and s u g g e s t e d t h a t c a v i t a t i o n may o c c u r i f t h e

p r e s s u r e f a l l s t o vapour p r e s s u r e f o r more t h a n 0.1%

of the t ime. T h i s l i m i t can be used t o o b t a i n a very

approximate g u i d e a s t o when c a v i t a t i o n might be

expec ted t o develop on t h e f l o o r of a s t i l l i n g b a s i n .

Assuming an r m s p r e s s u r e f l u c t u a t i o n of 9% of t h e

ups t ream v e l o c i t y head, a Gauss ian d i s t r i b u t i o n , and a

mean a b s o l u t e p r e s s u r e of 13m head of w a t e r , l e a d s t o

a l i m i t i n g v e l o c i t y of abou t 30m/s. For s i l l s and

b a f f l e b l o c k s , a h i g h e r t u r b u l e n c e l e v e l of 27% would

i n d i c a t e t h a t c a v i t a t i o n might occur a t v e l o c i t i e s

above abou t 17m/s. A s e x p l a i n e d above, a l l t h e s e

assumpt ions a r e a f f e c t e d by changes i n t h e f low

c o n d i t i o n s and t h e c o n f i g u r a t i o n of t h e b a s i n , s o e a c h

c a s e needs t o be a s s e s s e d i n d i v i d u a l l y .

Another f a c t o r t o be c o n s i d e r e d i s the f a v o u r a b l e

e f f e c t which e n t r a i n e d a i r h a s on reduc ing c a v i t a t i o n

damage ( s e e S e c t i o n 8 ) . S e l f - a e r a t i o n on long

s p i l l w a y s , t h e u s e of a e r a t o r s , and e n t r a i n m e n t a t t h e

jump i t s e l f may a l l c o n t r i b u t e t o r educ ing t h e danger

of c a v i t a t i o n i n s t i l l i n g b a s i n s .

Chute b locks and b a f f l e b l o c k s a r e the f e a t u r e s most

v u l n e r a b l e t o c a v i t a t i o n damage i n h y d r a u l i c jump

b a s i n s , because they a r e s u b j e c t t o t h e h i g h e s t

v e l o c i t i e s and produce t h e l a r g e s t p r e s s u r e

f l u c t u a t i o n s . Thus, a l t h o u g h they a l l o w t h e use o f

s h o r t e r b a s i n s , they a r e o f t e n o m i t t e d i n high-head

i n s t a l l a t i o n s . To be e f f e c t i v e , b l o c k s need t o have

h i g h d r a g c o e f f i c i e n t s (Cd), but t h i s a l s o r e s u l t s i n

h i g h v a l u e s of t h e c a v i t a t i o n i n c e p t i o n parameter K i ;

rounding t h e c o r n e r s reduces K bu t a l s o Cd. Shapes i

of b a f f l e b locks i n v e s t i g a t e d by Oskolkov h Semenkov

(1979) and by Rozanova h A r i e l (1983) a r e shown i n

F i g u r e 7. C a v i t a t i o n damage can be reduced o r a v o i d e d

by u s i n g a s u p e r - c a v i t a t i n g d e s i g n which c a u s e s t h e

f low t o s e p a r a t e a t t h e upst ream f a c e and form a l a r g e

f i x e d c a v i t y t h a t e n c l o s e s t h e b lock; damage i s

avo ided by removing t h e s o l i d s u r f a c e s from t h e r e g i o n

i n which t h e i n d i v i d u a l c a v i t y bubbles c o l l a p s e . T h i s

can be ach ieved by s l o p i n g t h e s i d e s of t h e b lock away

from the flow in the downstream direction and by

introducing a step in the floor (see, for example,

Type 1 in Figure 7).

Sudden expansions in high-head tunnels can be used to

convert kinetic energy to turbulence. Cavities are

liable to be formed around the perimeter of the high

velocity jet, and can damage the walls of the chamber

if they are too close. The performance of the

expansion chamber can be affected by small changes in

configuration, and model tests are normally necessary.

Information from several studies is given in Appendix

D, but direct comparisons of the results are difficult

because the cavitation numbers were defined in a

variety of ways.

7 UATERIALS

Cavitation tests carried out in the laboratory enable

the relative resistances of different materials to be

assessed. However, it is seldom possible to compare

results from different laboratories on a quantitative

basis because of variations in the types of equipment

and experimental techniques used. Methods have been

proposed for predicting from laboratory data the

amount of erosion that will occur under prototype

conditions, but they do not appear to be generally

applicable. Therefore, for the present at least, it

is necessary to rely on comparative tests and previous

prototype experience when selecting appropriate

materials for hydraulic structures.

The cavitation resistance of concrete is determined by

the internal cohesion of the binder and by the

adhesion between the binder and the aggregate; the

strength of the aggregate itself is not usually a

factor. Comprehensive laboratory tests carried out by

Inozemtsev et a1 (1965) indicated that best results

are obtained if the aggregate is porous, if the cement

and aggregate are as similar as possible, and if the

aggregate reacts chemically with the cement.

Many studies have shown that cavitation resistance

increases as the compressive strength M of the

concrete increases; Jiang S Chen (1982). for example,

found that for a given intensity of cavitation the

rate of material loss was proportional to M-4.84.

Kudriashov et a1 (1983) presented data on allowable

flow velocities over concrete; the results can be

approximated by the relation:

V = 3.0 + 0.43 M , for 20 < M < 50 MPa (11)

where V is the velocity in m/s above which cavitation

damage will occur, and M is the compressive strength

in MPa.

The resistance of ordinary concrete can be increased

by grinding the cement to make the particles finer;

this produces a denser mortar which adheres more

strongly to the aggregate. A similar effect is

achieved if very fine silica particles are added to

sulphate-resisting portland cement. A different

method of producing a dense surface finish is to cast

concrete against absorptive formwork; Galperin et a1

(1977) mention the successful use of panels lined with

timber-fibre sheets covered with dense coarse calico.

Adding steel fibres to concrete can increase its

cavitation resistance by a factor of about three.

Schrader S Munch (1976) describe the satisfactory use

of concrete containing 1% of 25mm long steel fibres

for replacing areas of ordinary concrete damaged by

cavitation. The fibres help the concrete to absorb

high-frequency fluid impacts without suEfering fatigue

failure, but the material may still be eroded by the

grinding action of debris in the flow.

A s i m i l a r improvement i n c a v i t a t i o n r e s i s t a n c e can be

o b t a i n e d by po lymer iz ing c o n c r e t e . The t e c h n i q u e i s

d e s c r i b e d by Murray 6 S c h u l t h e i s (1977) and S t e b b i n s

(1978) , and c o n s i s t s oE soak ing an a r e a of cu red

c o n c r e t e w i t h a monomer which i s then polymerized by

t h e a p p l i c a t i o n of h e a t . The method i s e f f e c t i v e i n

producing a good bond a t j o i n t s and r e p a i r s , b u t

c o n s i d e r a b l e e f f o r t may be needed t o e n s u r e t h a t t h e

c o n c r e t e i s f r e e of m o i s t u r e b e f o r e i t i s soaked w i t h

t h e monomer. Concrete c o n t a i n i n g s t e e l f i b r e s can

a l s o be polymerized, and t h i s f u r t h e r enhances i t s

c a v i t a t i o n r e s i s t a n c e . Other examples of t h e use of

f i b r o u s and polymerized c o n c r e t e s a r e mentioned i n

Appendix E.

P r a c t i c a l a s p e c t s of c o n s t r u c t i n g c o n c r e t e s t r u c t u r e s

which may be l i a b l e t o c a v i t a t i o n a r e cons ide red by

Schrader (1983). Reinforcement shou ld be des igned s o

a s t o e a s e t h e p l a c i n g of t h e c o n c r e t e , because

o t h e r w i s e t h e r e may be a tendency t o use t o o wet a

mix. Attempts t o o b t a i n a smooth f i n i s h by

overworking newly-placed c o n c r e t e weaken t h e s u r f a c e

and can l e a d t o c r a z i n g . Al though i t may be n e c e s s a r y

t o chamfer i r r e g u l a r i t i e s i n o r d e r t o r educe t h e i r

c a v i t a t i o n p o t e n t i a l ( s e e S e c t i o n 4 ) . t h e g r i n d i n g

p r o c e s s can weaken t h e a g g r e g a t e p a r t i c l e s a t t h e

s u r f a c e and a l l o w them t o be plucked o u t more e a s i l y

by t h e f low; t h e consequent roughening of t h e s u r f a c e

may a l s o promote c a v i t a t i o n downstream.

Epoxy and p o l y e s t e r r e s i n s have good p r o p e r t i e s of

s t r e n g t h and adhes ion , and can be a p p l i e d e i t h e r n e a t

i n t h e form of p r o t e c t i v e l a y e r s , o r mixed w i t h i n e r t

f i l l e r s t o produce m o r t a r s . Epoxy m o r t a r s have been

widely used f o r r e p a i r i n g o r r e p l a c i n g a r e a s of

c o n c r e t e damaged by c a v i t a t i o n , but t h e r e f e r e n c e s

d e t a i l e d i n S e c t i o n E.3 of Appendix E i n d i c a t e t h a t ,

i n g e n e r a l , they have no t performed w e l l . I t i s

p o s s i b l e , however, t h a t t h e f a i l u r e s may have r e c e i v e d

more a t t e n t i o n than t h e s u c c e s s e s . Three types of

problem have c o n t r i b u t e d t o t h e f a i l u r e s :

1. i n a p p r o p r i a t e f o r m u l a t i o n of r e s i n o r

mor ta r ;

2. i n s u f f i c i e n t s t a n d a r d s of c o n t r o l on s i te ;

3 . i n c o m p a t i b i l i t y of p h y s i c a l c h a r a c t e r i s t i c s .

The d e s i g n of a r e s i n o r mortar r e q u i r e s s p e c i a l i s t

knowledge, and s h o u l d be t a i l o r e d t o t h e s p e c i f i c

needs of each job; p a r t i c u l a r c o n s i d e r a t i o n should be

g i v e n t o t h e e f f e c t of m o i s t u r e , e i t h e r p r e s e n t

n a t u r a l l y o r g e n e r a t e d d u r i n g c u r i n g . To o b t a i n

s a t i s f a c t o r y r e s u l t s on s i t e , i t is n e c e s s a r y t o

c o n t r o l q u a n t i t i e s p r e c i s e l y , and t o adop t h i g h e r

s t a n d a r d s of mixing and p l a c i n g than a r e n e c e s s a r y

when working w i t h o r d i n a r y c o n c r e t e . One of t h e main

f a c t o r s c a u s i n g f a i l u r e s of r e p a i r s has been

d i f f e r e n t i a l thermal expans ion between t h e epoxy and

t h e su r round ing c o n c r e t e , l e a d i n g t o f a i l u r e of t h e

c o n c r e t e benea th t h e j o i n t and subsequent l o s s of t h e

epoxy pa tch . Other problems have been caused by epoxy

and c o n c r e t e hav ing d i f f e r e n t s u r f a c e t e x t u r e s , and by

t h e tendency f o r an epoxy p a t c h t o p r o j e c t above t h e

s u r r o u n d i n g c o n c r e t e a s a r e s u l t of t h e g r e a t e r

h a r d n e s s of t h e epoxy. I n t h e c a s e of m o r t a r s , some

of t h e s e problems can be reduced by s u i t a b l e c h o i c e s

of f i l l e r .

The a d d i t i o n of a r e l a t i v e l y s m a l l amount of polymer

t o c o n c r e t e can i n c r e a s e i t s c a v i t a t i o n r e s i s t a n c e

considerably. Test data given by Inozemtsev et a1

(1965) and Galperin et a1 (1977) showed that the

resistance of plastic concretes was 10-100 times that

of normal cement concrete; an epoxy-thiokol plastic

concrete had a performance similar to that of steel.

Steel linings are often used downstream of gates in

high-head tunnels, where the boundary layers have not

developed sufficiently to protect the walls from high

velocity flows. Information from several sources is

presented by Knapp et a1 (1970) on the comparative

resistancea of different metals to cavitation damage;

a representative selection of the data is given in

Section E . 2 . The resistance of alloyed steels can

vary widely, depending upon the chemical content and

whether they are forged, cast or rolled. Cavitation

can also accelerate the corrosive effects of water,

perhaps by stripping the protective oxide layer away

from the surface of the metal.

Information on the length of steel lining needed

downstream of a gate or orifice is limited, but an

ICOLD Committee (1986) recommended, for flow

velocities exceeding 25m/s, the following distances:

floor - 50 R full wetted height of side walls - 15 R half wetted height of side walls - 30 R

where R is the hydraulic radius of the orifice or gate

opening. The use of steel to armour chute blocks and

baffle blocks in stilling basins has not, in general,

proved successful because of the difficulty of

fixing .

Several types of protective lining for concrete or

steel have been tested, but aost suffer from

inadequate bond. Abelev et a1 (1971) found that a

l a y e r of n y r i t e a p p l i e d t o carbon s t e e l s i g n i f i c a n t l y

reduced t h e amount of e r o s i o n by c a v i t a t i o n . Wagner &

J a b a r a (1971) r e p o r t e d t h a t , i n US Bureau of

Reclamat ion e x p e r i e n c e , a neoprene compound was found

t o be t h e on ly s u i t a b l e c o a t i n g m a t e r i a l ; however, i t

r e q u l r e d c a r e f u l a p p l i c a t i o n i n a l a r g e number of t h i n

c o a t s .

8 AERATION

8.1 S e l f - a e r a t i o n

L a b o r a t o r y s t u d i e s and p r o t o t y p e e x p e r i e n c e have shown

t h a t t h e p r e s e n c e of a i r i n wa te r can reduce o r

e l i m i n a t e c a v i t a t i o n damage. The c o n c e n t r a t i o n of a i r

needed t o p r e v e n t damage was found by P e t e r k a (1953)

and o t h e r r e s e a r c h e r s ( s e e S e c t i o n F . l of Appendix F)

t o be abou t 7-8%. A s a r e s u l t of t h e s e l a b o r a t o r y

tests, i t h a s g e n e r a l l y been assumed t h a t a n a i r

c o n c e n t r a t i o n of a t l e a s t 7 4 % i s r e q u i r e d a d j a c e n t t o

p r o t o t y p e s t r u c t u r e s i n o r d e r t o p r o t e c t them a g a i n s t

c a v i t a t i o n . However, exper iments c a r r i e d o u t by Clyde

& T u l l i s (1983) on o r i f i c e s i n p i p e s i n d i c a t e t h a t t h e

l i m i t i n g a i r c o n c e n t r a t i o n necessa ry t o p r e v e n t

c a v i t a t i o n may be s u b j e c t t o s i g n i f i c a n t s c a l e

e f f e c t s ; f o r a g i v e n o r i f i c e r a t i o , i t was found t h a t

i n c r e a s i n g t h e p i p e s i z e o r d e c r e a s i n g t h e f low

v e l o c i t y both s e r v e d t o reduce t h e l i m i t i n g a i r

c o n c e n t r a t i o n ( f o r d e t a i l s s e e S e c t i o n G.2 i n Appendix

G). Such s c a l e e f f e c t s cou ld have a n i m p o r t a n t

b e a r i n g on t h e d e s i g n of a e r a t o r s ( s e e l a t e r ) , b e c a u s e

t h e i r s i z e and s p a c i n g a r e o f t e n de te rmined by t h e

requ i rement t o produce a c e r t a i n minimum a i r

c o n c e n t r a t i o n .

A i r can be e n t r a i n e d by t u r b u l e n c e a t t h e s u r f a c e of

h i g h - v e l o c i t y f lows . The buoyancy of t h e a i r bubbles

t e n d s t o be c o u n t e r a c t e d by t h e f l u i d t u r b u l e n c e , and

t h i s can cause them t o d i f f u s e downwards a s they a r e

c a r r i e d along by the flow. The f l o o r of the channel

w i l l be protected from poss ib le c a v i t a t i o n damage if

t h i s se l f - ae ra t ion process produces a s u f f i c i e n t

concent ra t ion of a i r a t the bed.

There i s general agreement tha t s e l f - ae ra t ion begins

on a spi l lway a t a point where the boundary layer has

grown s u f f i c i e n t l y f o r i t s thickness t o be nea r ly

equal t o the depth of flow. Theore t ica l and

experimental r e s u l t s obtained by Wood e t a 1 (1983) and

Wood (1985) can be combined to produce the following

equation f o r the d is tance L to the point of incep t ion i

of a i r entrainment:

The d i s t ance L . is measured along the spi l lway from 1

t he c r e s t ; g i s the acce le ra t ion due t o g r a v i t y , q i s

the discharge per un i t width, k is the Nikuradse sand S

roughness of the channel, and H i s the v e r t i c a l S

d i s t ance from the r e se rvo i r l e v e l t o the water s u r f a c e

i n the channel. Prototype measurements of the

incept ion d is tance on high-head spi l lways a r e given by

Galperin e t a 1 (1977); va lues of L var ied from 30m i

a t a un i t discharge of q = 4 . 2 m 3 / s / m t o lO0m a t

q = 18.5m3/s/m.

The growth of the boundary layer i s not the only

f a c t o r governing the s t a r t of a e r a t i o n , because the

entrainment process requi res the flow t o have

s u f f i c i e n t turbulent energy a t the f r e e su r face to

overcome the e f f e c t s of sur face tension. Severa l

i n v e s t i g a t o r s have produced c r i t e r i a f o r descr ib ing

the condit ions a t the onset of a e r a t i o n , and these a r e

l i s t e d i n Sect ion G.2 of Appendix G. Three of the

c r i t e r i a a r e expressed i n terms of the Froude number

of the flow, and i n d i c a t e tha t entrainment w i l l begin

if the value is greater than about F = 5-6. The

physical significance of the Froude number in

determining the start of aeration is not clear, but

its use appears justified because both model and

prototype data indicated similar limiting values of

F.

The concentration of air in the flow increases with

distance downstream of the inception point, and

eventually reaches an equilibrium value, provided the

channel is long enough and is of constant slope.

Various formulae have been developed for estimating

the depth-averaged equilibrium air concentration C, and details of these are given in Section F.2 of

Appendix F. The equations have widely differing

forms, and can therefore only properly be compared on

the basis of independent prototype measurements, which

were not available for this review. In the absence of

such data, it is suggested that estimates of C for spillways be calculated from several of the formulae

(e.g. Equations F.6, F.7, F.16, F.19, F.24, and the

data of Wood (1983) tabulated in Section F.2), and

compared to establish a "likely" value. For air

entrainment in steep partially-filled pipes, the only

equation for appears to be that due to Volkart

(1982), Equation F.21; this result was obtained using

both model and prototype data. It should be noted

that some researchers have defined concentration in

terms of the volumes of air and water ( C I ) , and others -

in terms of their rates of flow ( C 2 ) , see Equations

F.4 and F.5; in cases where the quantity was not

precisely defined, the symbol has been used in

Appendix F.

An analysis by Wood (1983) of laboratory results

obtained by Straub & Anderson (1958) indicated that

the vertical dfstribution of air at a point along a

channel is determined only by the local value of the

- mean air concentration C at that point; this finding

applies at all points and not just far downstream

where the flow has reached an equilibrium state. The

results show that in order to obtain an air

concentration at the bed of 7% (so as to avoid

possible cavitation damage), the mean air

concentration needs to be about 30%; such a figure

will not be achieved if the slope of the channel is

less than about 22.5'.

Many spillways are not long enough for the aerated

flow to reach an equilibrium state. Numerical models

for determining the developing region of air

entrainment have been developed by Wood (1985) and by

Ackers h Priestley (1985), and have been calibrated

against laboratory and prototype data (for unit

discharges of up to 3.2m3/s/m). Details of the models

are given in Section F.2 of Appendix F.

The research that has been carried out on

self-aeration indicates that, in favourable

circumstances, enough air can be entrained to prevent

cavitation damage. However, the distance required for

air to reach the bed of a channel increases rapidly

with increasing discharge. The mechanism may

therefore provide protection at low unit discharges

(e.g. < 5m3/s/m), but not the larger flows for which

most spillways are designed. However, all cases

should be investigated on an individual basis in order

to estimate the likely effects of self-aeration.

8.2 Aerators on

spillways

If the tolerances on the surface finish required to

avoid cavitation are too severe to be practicable, and

there is not enough self-aeration, possible damage to

a channel may be prevented by using an aerator to

s u p p l y a i r around t h e p e r i m e t e r . The a i r can be

pumped under p r e s s u r e , but n e a r l y a l l a e r a t o r s work by

c r e a t i n g a s u c t i o n which i s used t o draw t h e a i r

n a t u r a l l y from t h e a tmosphere . Such a e r a t o r s c o n s i s t

of a n o f f s e t o r d e f l e c t o r which causes t h e f low t o

s e p a r a t e from t h e s u r f a c e of t h e channe l and form a

l a r g e a i r c a v i t y . The wa te r p a s s i n g over t h e c a v i t y

e n t r a i n s a i r s t r o n g l y , and the reby produces t h e

n e c e s s a r y sub-atmospher ic p r e s s u r e .

T y p i c a l f e a t u r e s of a e r a t o r s a r e shown i n F i g u r e 8 ,

and c a n comprise d e f l e c t o r s , o f f s e t s , no tches o r

s l o t s , e i t h e r s i n g l y o r i n combinat ion. D e f l e c t o r s

t e n d t o produce s t r o n g a e r a t i o n , b u t may d i s t u r b t h e

f low c o n s i d e r a b l y . An o f f s e t c a u s e s l e s s d i s t u r b a n c e ,

b u t needs t o be l a r g e r than a d e f l e c t o r i n o r d e r t o

p r o v i d e t h e same a i r demand. I f a n e x i s t i n g s t r u c t u r e

r e q u i r e s m o d i f i c a t i o n s t o p reven t c a v i t a t i o n damage,

i t i s u s u a l l y e a s i e r t o i n c o r p o r a t e a d e f l e c t o r than

an o f f s e t . Means of s u p p l y i n g a i r t o a n a e r a t o r

i n c l u d e d u c t s d i s c h a r g i n g a t t h e base of t h e s i d e

w a l l s o r a t p o i n t s a c r o s s t h e f l o o r of t h e channel .

A l t e r n a t i v e l y , d e f l e c t o r s and o f f s e t s i n s i d e w a l l s

c a n be added s o a s t o a l l o w a i r t o r each a e r a t o r s

l o c a t e d i n t h e c h a n n e l f l o o r s ; s i m i l a r use can a l s o

be made of p i e r s and w a l l s w i t h b l u n t ends which

c r e a t e v e r t i c a l s e p a r a t i o n pocke t s i n t h e f low. Some

examples of t h e s e types of ar rangement a r e shown i n

F i g u r e 9.

The requ i rements of a n e f f e c t i v e a e r a t i o n system a r e

t h a t :

1. i t s a i r demand should be s u f f i c i e n t t o g i v e

l o c a l a i r c o n c e n t r a t i o n s a t t h e channe l

boundar ies t h a t a r e h i g h enough t o p r e v e n t

c a v i t a t i o n damage (e.g. C > 7 % ) ;

2. t h e a i r c a v i t y produced by Ehe d e v i c e should

remain s t a b l e over t h e f u l l r ange of

o p e r a t i n g c o n d i t i o n s and shou ld no t end t o

f i l l w i t h w a t e r ;

3. t h e a e r a t o r shou ld n o t produce t o o g r e a t a

d i s t u r b a n c e of t h e f low o r a n e x c e s s i v e

amount of sp ray ;

4. t h e s p a c i n g between s u c c e s s i v e a e r a t o r s

should be such t h a t t h e l o c a l a i r

c o n c e n t r a t i o n a t t h e f l o o r does not f a l l

below t h e amount r e q u i r e d t o p r o t e c t a g a i n s t

c a v i t a t i o n damage.

Model and p r o t o t y p e d a t a o b t a i n e d i n a s e r i e s of

s t u d i e s by P i n t o (1979) . P i n t o e t a 1 (1982) and P i n t o

h N e i d e r t (1982, 1983a) have he lped t o i d e n t i f y t h e

f a c t o r s which d e t e r m i n e t h e amount of a i r e n t r a i n e d by

a n a e r a t o r . The most i m p o r t a n t a r e t h e l e n g t h L o f C

t h e a i r c a v i t y (measured from t h e a e r a t o r t o t h e p o i n t

where t h e f low r e - a t t a c h e s ) , and t h e v e l o c i t y V of t h e

wa te r j u s t ups t ream of t h e a e r a t o r . The s t u d i e s

showed t h a t t h e r a t e of a i r demand (q ) p e r u n i t w i d t h a

of c h a n n e l can be d e s c r i b e d by t h e e q u a t i o n :

The v a l u e of t h e non-dimensional c o e f f i c i e n t k depends

upon t h e geometry of t h e a e r a t o r , and on s e v e r a l o t h e r

f low paramete r s which a r e d e t a i l e d i n S e c t i o n F.3 of

Appendix F. One of t h e most i m p o r t a n t of t h e s e i s t h e

amount Lp by which t h e p r e s s u r e i n t h e a i r c a v i t y i s

below t h a t a t t h e f r e e s u r f a c e . For a g i v e n a i r

demand, t h e p r e s s u r e d i f f e r e n c e & i s determined by

t h e head- loss c h a r a c t e r i s t i c s of t h e a i r supp ly

system. However, i t s e l f h e l p s t o d e t e r m i n e t h e a i r

demand because it affects the value of k in Equation

13 and also the length of the air cavity. Therefore,

when considering the performance of an aerator, it is

always necessary to take the particular

characteristics of the air supply system into

account.

Despite tne interactions between these various

factors, it appears that Equation 13 may still provide

a useful basis for determining the performance of a

given aeration system. Pinto et a1 (1982) obtained

model and prototype data for aerators at Foz do Areia

Dam (Brazil), and found that the values of k remained

approximately constant over a six-fold range of water

discharges. For air supplied laterally from both

sides of the channel the value was k = 0.033, and for

supply from one side only it was k = 0.023.

Independent confirmation of the validity of Equation

13 was provided by Pan et a1 (1980), who obtained

fairly similar values of k using theoretical and

experimental results. However, each design of aerator

needs to be considered on an individual basis, because

the value of k may vary considerably according to the

particular characteristics of the system.

Analytical or empirical methods of determining the

length of air cavity formed by an aerator have been

developed by several researchers (see Section F.3).

The equations are valid only for two-dimensional flows

in channels of constant slope. The analytical

solutions contain various simplifying assumptions, but

the one obtained by Schwarz 6 Nutt (1963) has an

advantage in that it takes account of the pressure

difference 4, between the upper and lower surfaces of

the nappe. Numerical solutions of Laplace's equation

have been used to determine trajectories at aerators

(e.g. Wei 6 De Fazio (1982)), and such techniques are

capable of allowing for three-dimensional effects and

channel curvature. Analytical and numerical methods

do not take account of air resistance and turbulence,

and may therefore tend to over-estimate the length of

the air cavity.

Dimensions and characteristics of some aerators which

have been used in prototype installations are given in

Table 3. Prusza et a1 (1983) recommend that the mean

air concentration produced by an aerator should be

limited to 2 = 40-50% in order to prevent atomisation

of the flow; at this limit the length of the cavity

will be about 3-5 times the water depth. Values of

the pressure difference 4, for aerators supplied by

air ducts are typically between 0.5m and 2.0172 head of

water. High air velocities in ducts supplying

aerators should be avoided, because they can cause

objectionable noise; Falvey (1980) recommends maximum

velocities of 30m/s for continuous operation, and

90m/s for short durations. The required spacing

between successive aerators is determined by the rate

at which the local air concentration near the floor of

the channel decreases with distance. Prototype data

from several Russian dams (see Section F.3) suggest

that, in a straight channel, the mean air

concentration decreases at a rate of between 0.2% and

0.8% per metre; in channels with convex curvature,

the loss rate can increase to 1.5% per metre due to

the effects of centripetal pressure. Distances

between aerators are typically in the range 30-100m.

Prototype data obtained by Pinto (1986) for the Foz do

Areia spillway indicate that factors not highlighted

by.mode1 tests may contribute to the effectiveness of

aerators in preventing cavitation damage.

Measurements of flow depths along the channel showed

that considerable entrainment occurred at the

aerators, but that only a small proportion of the air

(of the order of 25% or less) was supplied directly by

the aerators. The remainder was entrained at the

surface as a result of the strong turbulence created

in the flow by the presence of the aerators. Results

such as these suggest that a more efficient method of

preventing cavitation damage might be to use smaller

but more closely-spaced devices that cause less

disturbance to the flow.

8.3 Tunnels

Aerators are often located immediately downstream of

gates in high-head tunnels in order to protect the

walls and floors from cavitation damage, and these

operate in a similar way to aerators in spillways.

Ducts may be used to supply air to an offset in the

floor or, for example, to the seating of a radial gate

with recessed seals. For tunnels flowing partly full,

a more common arrangement is to form, just downstream

of the gate, a vertical U-shaped slot in the walls and

invert so as to allow air from above the water surface

to reach the invert.

Recommendations on the design of aerators for tunnels

are given by Beichley 6 King (1975) as follows:

1. Offsets in the wall and floor are normally

preferable to deflectors and air slots;

2. Deflectors may be the only option when

modifying an existing structure;

3. Offsets at the floor and at the side walls

should be respectively 116 and 1/12 of the

frame width of the gate (with a minimum of

100mm) ;

4. Wall deflectors need to be used in

conjunction with air slots if the downstream

sides of the tunnel are parallel;

5. Air slots should be square in cross-section,

and a size of 300mm X 300mm should be

adequate for gates measuring up to 1.2m X

2.3m with heads of up to 100m.

Further details are given in Section F.4 of Appendix

F. A potential problem that can arise with aerators

in tunnels is that, at the walls, they can produce

fins of water which may be large enough to seal the

conduit. To avoid this effect it may be necessary to

limit the size of the offsets or deflectors.

High-velocity water flowing in a tunnel can draw large

quantities of air along with it. If this "natural"

air demand is not satisfied, the ambient pressure

downstream of the gate may be reduced significantly

below atmospheric (increasing the risk of cavitation).

and undesirable surging may also occur. In large

tunnels the necessary air is often supplied by a

system of ducts or galleries connecting the downstream

side of the gate to the atmosphere. Use of an aerator

creates an additional "forced" demand which can

normally be met by the same supply system.

It is important, when considering the "natural" air

demand, to distinguish cases where a tunnel downstream

oE a gate flows part-full over its full length from

those where the tunnel is sealed by a hydraulic jump;

in the latter cases the air flow is determined by the

amount of entrainment in the jump and by the capacity

of the flow to transport the bubbles of air along the

tunnel.

Many r e s e a r c h e r s have f i t t e d d a t a on t h e " n a t u r a l " a i r

demand i n t u n n e l s t o a n e q u a t i o n of t h e form:

where F i s t h e va lue of t h e Froude number a t t h e vena C

c o n t r a c t a downstream of t h e g a t e . Values of 0 g i v e n

by some of t h e r e s u l t i n g e q u a t i o n s a r e p l o t t e d i n

F i g u r e 10, and i t can be seen t h a t t h e p r e d i c t i o n s

vary c o n s i d e r a b l y . I n g e n e r a l , i t i s found t h a t

t u n n e l s f l o w i n g f r e e l y produce h i g h e r a i r

c o n c e n t r a t i o n s than t u n n e l s s e a l e d by h y d r a u l i c jumps.

Also, i t appears t h a t p r o t o t y p e v a l u e s of p a r e

somewhat h igher than those measured i n e q u i v a l e n t

models. Without a c l o s e s tudy of t h e o r i g i n a l d a t a ,

i t i s d i f f i c u l t t o i d e n t i f y t h e r e a s o n s f o r t h e

d i s c r e p a n c i e s . I n t h e i n t e r i m , a i r c o n c e n t r a t i o n s f o r

p r o t o t y p e t u n n e l s wi th jumps might be e s t i m a t e d from

t h e US Army Corps of E n g i n e e r s (1964) e q u a t i o n ( w i t h

a = 0.03 and m = 1.06 i n Equa t ion 1 4 ) . However, i t

s h o u l d b e borne i n mind t h a t t h e r e s u l t s of a few

s t u d i e s would s u g g e s t somewhat h i g h e r v a l u e s of p ( f o r

d e t a i l s , see S e c t i o n F.4 o f Appendix F). For t u n n e l s

f l o w i n g f r e e l y , Sharma's (1976) e q u a t i o n

might be used.

A t s m a l l g a t e open ings , sp ray- type f low may o c c u r , and

t h i s can g i v e rise t o l a r g e v a l u e s of p. However,

s i n c e t h e d i s c h a r g e of water i s low under t h e s e

c o n d i t i o n s , t h e t o t a l a i r f low w i l l g e n e r a l l y be less

t h a n a t l a r g e r g a t e open ings .

I f a n a e r a t o r i s used i n a ga ted t u n n e l , t h e

a d d i t i o n a l a i r demand t h a t i t c r e a t e s shou ld be

a s s e s s e d s e p a r a t e l y . The a i r supp ly system shou ld be

s i z e d t o c a t e r f o r t h e combined " n a t u r a l " and " f o r c e d "

a i r demands.

9 MODELLING

S t u d i e s of c a v i t a t i o n can be c a r r i e d ou t a t a reduced

s c a l e i n t h r e e main ways. F i r s t l y , a model may be

o p e r a t e d a t a tmospher ic p r e s s u r e a c c o r d i n g t o t h e

Froud ian s c a l i n g law. P r e s s u r e s a l o n g t h e boundar ies

of t h e f low a r e measured and s c a l e d t o p r o t o t y p e

c o n d i t i o n s . C a v i t a t i o n i s p r e d i c t e d t o occur i f t h e

s c a l e d p r e s s u r e a t a p o i n t r e a c h e s t h e vapour p r e s s u r e

of wa te r . The p r e s s u r e t a p p i n g s shou ld be l o c a t e d so

a s t o i d e n t i f y t h e p o i n t s of minimum p r e s s u r e , and

accoun t should be t aken of b o t h t h e mean and

f l u c t u a t i n g p r e s s u r e components. The method w i l l

under -es t ima te t h e l i k e l i h o o d of c a v i t a t i o n i f f low

s e p a r a t i o n o c c u r s , because t h e lowes t p r e s s u r e s w i l l

b e l o c a t e d i n t h e body of t h e f l u i d and no t a t t h e

boundar ies .

The second kind of t e s t is c a r r i e d o u t i n a c a v i t a t i o n

t u n n e l , i n which t h e p r e s s u r e i n t h e working s e c t i o n

i s reduced below a tmospher ic s o a s t o o b t a i n e q u a l

v a l u e s i n model and p r o t o t y p e of t h e pa ramete r K

d e f i n e d i n Equa t ion 2 . T h i s method e n a b l e s t h e

o c c u r r e n c e of c a v i t a t i o n i n t h e model t o be d e t e c t e d

d i r e c t l y , and i s s u i t a b l e f o r b o t h s e p a r a t i n g and

non-separa t ing f lows. S i n c e t h e working s e c t i o n f lows

f u l l , t h e t e c h n i q u e i s n o t a p p r o p r i a t e where

f r e e - s u r f a c e e f f e c t s a r e impor tan t (e.g. a t b a f f l e

b locks i n s t i l l i n g b a s i n s ) . Having e q u a l v a l u e s of K

i n model and p r o t o t y p e does n o t n e c e s s a r i l y e n s u r e

complete dynamical s i m i l a r i t y , and model r e s u l t s may

s t i l l be s u b j e c t t o some s c a l e e f f e c t s .

The t h i r d way of s t u d y i n g c a v i t a t i o n i s t o u s e a

vacuum t e s t r i g i n which t h e a i r p r e s s u r e can be

reduced below atmospher ic . T h i s a l l o w s models w i t h

f r e e - s u r f a c e f lows t o be o p e r a t e d a t p r o t o t y p e v a l u e s

of K. I n g e n e r a l , vacuum r i g s p rov ide t h e b e s t means

of c a r r y i n g o u t c a v i t a t i o n t e s t s , b u t they can be

expens ive t o c o n s t r u c t and d i f f i c u l t t o o p e r a t e .

R e s u l t s from model s t u d i e s of c a v i t a t i o n can b e

a f f e c t e d by t h e p r e s s u r e , v e l o c i t y and s c a l e a t which

t h e t e a t s a r e c a r r i e d o u t . S e v e r a l i n v e s t i g a t o r s have

found t h a t v a l u e s of t h e i n c i p i e n t c a v i t a t i o n index K i

t e n d t o i n c r e a s e w i t h i n c r e a s i n g s i z e of model, b u t

t h e r e i s c o n f l i c t i n g ev idence concern ing t h e e f f e c t s

of changes i n p r e s s u r e and v e l o c i t y ( f o r d e t a i l s , s e e

S e c t i o n G . l of Appendix G). O t h e r f a c t o r s which can

be s i g n i f i c a n t a r e t h e g a s and d u s t c o n t e n t s of t h e

w a t e r , and t h e number and s i z e of t h e n u c l e i t h a t i t

c o n t a i n s . These f a c t o r s i n f l u e n c e t h e v a l u e of t h e

c r i t i c a l p r e s s u r e p a t which c a v i t i e s b e g i n t o grow; C

a s e x p l a i n e d i n S e c t i o n 2 .2 , p i s u s u a l l y c l o s e t o C

bu t n o t e q u a l t o t h e vapour p r e s s u r e p of t h e w a t e r . v

K e l l e r (1984) developed a l a b o r a t o r y t e c h n i q u e f o r

measur ing p , and showed t h a t wa te r samples of C

d i f f e r e n t q u a l i t i e s gave c o n s i s t e n t v a l u e s of K i f i t h e s e were c a l c u l a t e d u s i n g p i n s t e a d of p . Use o f

C v t h i s t e c h n i q u e would a l l o w d a t a from d i f f e r e n t s t u d i e s

t o be s t a n d a r d i s e d , and would e n a b l e s c a l e e f f e c t s t o

be i d e n t i f i e d more p r e c i s e l y . However, i n o r d e r t o

a p p l y t h e l a b o r a t o r y r e s u l t s t o p r o t o t y p e c o n d i t i o n s ,

i t w i l l be n e c e s s a r y t o de te rmine v a l u e s of t h e

c r i t i c a l p r e s s u r e f o r t y p i c a l p r o t o t y p e f lows .

The f a c t t h a t wa te r w i l l no t e n t r a i n a i r u n l e s s t h e

v e l o c i t y and t u r b u l e n c e of t h e f low a r e g r e a t enough

d e m o n s t r a t e s c l e a r l y t h a t p r o t o t y p e a i r demands can be

under -es t ima ted by models which a r e too s m a l l .

However, i t i s n e c e s s a r y t o d i s t i n g u i s h between a i r

which i s e n t r a i n e d i n t o t h e f low by t u r b u l e n c e and a i r

which i s drawn a l o n g above t h e f r e e s u r f a c e . The

former i s r e l e v a n t t o s e l f - a e r a t i o n and t h e

performance of a e r a t o r s ; t h e l a t t e r can accoun t f o r a

s i g n i f i c a n t p r o p o r t i o n of t h e t o t a l a i r demand i n a

t u n n e l f lowing p a r t - f u l l .

Complete models of s p i l l w a y s a r e n o t s u i t a b l e f o r

p r e d i c t i n g s e l f - a e r a t i o n because i t i s n o t p o s s i b l e t o

s c a l e t h e i n c e p t i o n l e n g t h s c o r r e c t l y , and because t h e

v e l o c i t i e s a r e n o t u s u a l l y h i g h enough. Numerical

models based on p r o t o t y p e d a t a , such a s t h o s e

developed by Wood (1985) and Ackers h P r i e s t l e y

(1985) , o f f e r a b e t t e r means of e s t i m a t i n g t h e amount

of s e l f - a e r a t i o n ( s e e S e c t i o n F.2 o f Appendix F).

Large-sca le s e c t i o n a l models of a e r a t o r s i n s p i l l w a y s

have been used t o de te rmine t h e i r h y d r a u l i c

performance and t o e s t i m a t e t h e i r a i r demands.

S e c t i o n a l models a r e n e c e s s a r y because of t h e l i m i t e d

pumping c a p a c i t y a v a i l a b l e i n most l a b o r a t o r i e s , b u t

a l lowance may need t o be made f o r t h e e x t r a r e s i s t a n c e

and e n t r a i n m e n t produced by t h e s i d e w a l l s . T e s t s of

s i m i l a r models a t d i f f e r e n t s c a l e s , and comparisons

between model and p r o t o t y p e d a t a , i n d i c a t e t h a t

r e a s o n a b l e e s t i m a t e s of a i r demand can be o b t a i n e d

from a model i f i t s s c a l e i s 1:15 o r l a r g e r ( s e e

S e c t i o n G . 2 o f Appendix G f o r examples) , and i f t h e

f low v e l o c i t y i n t h e model exceeds abou t 6-7m/s.

However, f o r such a model t o g i v e r e l i a b l e r e s u l t s , i t

must a l s o reproduce c o r r e c t l y t h e head- loss

c h a r a c t e r i s t i c s of t h e a i r supp ly sys tem i n t h e

p r o t o t y p e . I f t h e s i z e s of t h e a i r d u c t s have n o t

been determined a t t h e t ime t h a t t h e model s t u d y i s

c a r r i e d o u t , t h e a e r a t o r shou ld be t e s t e d f o r a range

of p o s s i b l e head- loss c h a r a c t e r i s t i c s .

Numerous model s t u d i e s have been c a r r i e d o u t t o

p r e d i c t a i r demands i n g a t e d t u n n e l s , and comparisons

w i t h p r o t o t y p e measurements s u g g e s t t h a t s c a l e s o f

1:25 or larger will give satisfactory results (see

Section G.2 for examples). However, it is again

important that all the air and water passages should

be correctly reproduced in such models. Some

laboratory studies of air entrainment in tunnels

flowing freely have indicated that Froudian scaling is

inappropriate (see Section F.4); nevertheless,

several Froudian model studies have shown reasonable

agreement with prototype air demands.

Measurements of two-phase flows are difficult, and

most rely on indirect methods, e.g. the variation in

electrical current caused by the passage of air

bubbles or water droplets. In order to interpret such

signals, it is usually necessary to make assumptions

about the behaviour of two-phase flows that are

difficult to verify. Apparent discrepancies between

the results of different studies may thus be due to

instruments having different operating

characteristics. Examples of devices used to measure

velocities and air concentrations in aerated flows are

described in Section G.3 of Appendix G.

10 CONCLUSION

This review has indicated the very considerable amount

of work that has been carried out on cavitation and

aeration in hydraulic structures. The research has

identified the principal factors involved in both

problems, although the physical processes underlying

them are still imperfectly understood. Due to the

complexities, it has not been possible to plan many

experimental studies within a firm theoretical

framework. Inevitably, therefore, the results

sometimes disagree, and lead to empirical equations

which link the various factors in different ways.

This tends to make it difficult to give designers

hard-and-fast rules concerning the occurrence of

cavitation and methods of preventing it.

Nevertheless, there are areas of broad agreement, and

in several of the preceding sections it has been

possible to draw general conclusions which may be of

use in design.

Differences between results from studies of a

particular problem can be viewed in several ways. Are

they due to shortcomings in some of the experiments?

Can they help to explain the physical processes

involved? Are they significant in terms of practical

application?

A good example is provided by the tests which have

been carried out to determine the cavitation potential

of surface irregularities. Detailed comparisons for a

given shape of irregularity show that differences can

be caused by scale effects, and by variations in

turbulence, boundary layer thickness and water

quality. If these factors can be quantified and

explained, a better understanding of the fundamental

processes will have been obtained. However, such

differences may not be very large compared with the

effects produced by small changes in shape.

Construction faults in hydraulic structures cannot be

predicted accurately in advance, and their shapes will

seldom conform precisely to those tested in the

laboratory. Therefore, from the point-of-view of

designers, present knowledge may be sufficient to

enable them to assess the risks of cavitation with

reasonable accuracy.

Aerators have proved an effective means of reducing or

preventing cavitation damage in high-head spillways

and gated tunnels. However, our understanding of air

entrainment is less advanced than that of cavitation

inception. As a result, it is at present difficult to

predict the performance of a prototype aerator

theoretically, or to scale results from a physical

model reliably. Well-planned research on the

behaviour of a e r a t o r s i s t h e r e f o r e l i k e l y t o l e a d t o

worthwhi le improvements i n t h e d e s i g n of such

s t r u c t u r e s . D e t a i l e d recommendations f o r r e s e a r c h on

each of t h e main t o p i c s covered i n t h i s review a r e

g i v e n i n Appendix H.

11 ACKNOWLEDGEKENTS

The a u t h o r i s p l e a s e d t o acknowledge t h e a d v i c e and

encouragement r e c e i v e d from c o l l e a g u e s a t Hydrau l i c s

Resea rch , i n c l u d i n g p a r t i c u l a r l y M r J A P e r k i n s .

H e l p f u l comments on a d r a f t v e r s i o n of t h e review were

made by M r P Ackers , M r R E Coxon, D r R P Thorogood

and M r D G Wardle, and many of t h e i r s u g g e s t i o n s were

i n c o r p o r a t e d i n t h e f i n a l v e r s i o n . ICOLD k i n d l y

a s s i s t e d by r e q u e s t i n g , through i t s member

o r g a n i s a t i o n s , d e t a i l s of r e c e n t work on c a v i t a t i o n

and a e r a t i o n ; t h e good r e s p o n s e from many r e s e a r c h e r s

around t h e world enab led t h e review t o be made a s

up-to-date a s p o s s i b l e . F i n a l l y , many thanks a r e due

t o t h e t y p i n g s t a f f a t H y d r a u l i c s Resea rch , headed by

Mrs G B Baker, who coped w i t h c o n t i n u a l r e v i s i o n s of

t h e t e x t .

9690' 0

VOLO'O

ZILO'O

OZLO'O

8ZL0'0

SELO'O

ZVLO' 0

67L0'0

LSLO' 0

rn/N

(l?e/la2en)

uoysua~ asejmg

-

09L

VLS

EEV

EZE

8EZ

VL1

SZ1

68

Z 9

zalen 30 peaq mm

alnssald lnode~

OOVL

0095

OEZV

091E

OEEZ

OOL1

OEZI

OL8

019

zrn/N

E'Z66

1' 766

L'S66

I'L66

Z' 866

1'666

L' 666

0'0001

6' 666

Em/aY

dlysuaa

9-01 X 6S9'0

g-O1 X SZL'O

9-01 X Z08'0

9-01 X 768'0

9-01 X 700'1

9-01 X 8E1'1

9-01 X 70E.1

9-01 X 71S'I

9-01 X L8L.1

s/zm

daysossy~ sy~srnauy~

0 7

S E

0 E

S Z

OZ

S 1

0 1

S

0

3.

alnae~adrna~

TABLE 2: Values of Ki for Surface Irregularities Prom: Ball (1963)

a

C

cn

rl

m

" r

0

0

P

ILlD

?

F

E a:

m

m

-W

0

4

mm

m

n

b.

r

F

C

P

PL

O

WO

b

0

P n

W

P*.

m

I( v.

g 1

,. F

A m

r r

D

o

n"

m

W

r

SF

v

W

k

m

a

6 n

.a

"C

W

O

FF

,

k r

b.

g 0

;

W*

;

* l

IY

W@

W

"

r

F C

I

Z

r B

m F

0

0

W

" n

s r*

F

O

P

P

m

v n

0

n

(D

" n

e !. -

r r -- m

a0

g,'

U

C

rr

r

rr

rr

U

U

--

W-

rr

rr

rr

rr

r

rr

r

r

v

P

W

W

*.

U

N

U

,-C

U

U

N'C

U

er

r

cr

U

c

. ..

o

m

-

b"

.,L-

*P

"

U .

o

uu

ww

U

Y

uu

N

UU

W

UL

-U

W

-

W

W

U

- - ?

. P

?

P T

P?

P

P

?

a

WN

0

o

r

WN

ul

g P

P?

?

?

P?

?

??

P

P?

?

P?

P

P

b

WN

N

U

Nr

*

U*

-

rW

N

NY

S

. r

0

o

8X

8

2X

gg

8

m

OO

UO

*

OU

o

o

oo

o

09

o

o

8X

88

:S

8

88

S

g

U

P ?

P

r

? TT

c .

...

r

. .

Q *

U

N N

,U

0' 8:

U

*

"W

N

0

Q

O

L-0

I* 1

0

I

85

8

I

81

I

o

I

#m

m

10

o

o

m (

10

o

oo

U

r

0

m

l 1

r

l N

-

U

r

L-

m

*

a

0

Y

0

m

, Y

,

, L

-,

m,

0

G

%

ZZ

,

0,

W

,

,, ,

I ON,

0,

I

W

a

0

&:

ss

??

?

5 0

.

&'5"55

D

v.

.

P-

m

"W

*

FF

Z

m*

"

22

...m

!5

P

- $

4 r

e-

F

m

0

P-

- P m

n

P

- n

-

-m

P-

Dn

D

-*

"m

.

-P

-*

"

"m

P

-"

*

- "

... -..

. P

-

m.,

P-

m-

P

- m

-

*r

",

LP

-

- -

m

U-

., "

... m

0

a.........

... F

* F

P

-

- - -

., W

.,.,.,

4

m

L.

L.

yl

U

01

- .,

U

L-

I P

-

P-

.

0

I

r

P-

ro

.,

,

8 ,

2 4r

CP

-Y

m r

P-

g"

F,;

:>

P , m

:"h

D

m

P

rn

n

o5

Pm

"m

P- .

?L

;

FW

OO

Y

"*

P-

m

S

D "

m m

P

Fig 2 Cavi tat ion damage curve

Incipient damage parameter Kid

0 0 0 >

0 N r- z.

0

I 1 I I

-

- -

-

n 7 0

3 . . 0 LA X

0, X

-

0 < PO

- -

0 0 40'

v, m 3 m 7 X 0 < - 2 \D 4 \D

- -

- p

I l I I

! W xapu! uo!yel!neJ lua !d !~u l

Fig 4 Values o f K i f o r su r face i r regu lar i t ies

Fig 6 Cav i ta t ion p a r a m e t e r s o f g a t e s l o t s

q- ".A "bh$EgL& ,, S;?., -

(a ) Ramp and o f f s e t

Ramp o n l y t = o O f f s e t on ly h = o

(b) Ramp wi th groove and o f f s e t

( c ) Ramp wi th s l o t and o f f s e t

Fig 8 Types o f ae ra to r .

L .- <

0.1 0.08

O o 6 OOL /// ---- - Spray- f low Free-f low Flow with jump

- Range o f data

001 1 2 L 6 8 1 0 20 L0 60 80 100

Key Reference Eqn. Key Reference Eqn.

A Kalinske 8 Rober tson F.52 E Haindl F.69 B Campbell g Guyton F 5 4 F Wisner F.59

C U S . Army Corps Engrs. F.55 G Sharma F.62 D Ouazar g Lejeune F.67 H Wisner F.60

I Sharma F.63

Fig 10 Comparison o f p r e d i c t e d a i r demands i n tunne ls

APPENDIX A

SYMBOLS

Cross-sectional area of flow

Cross-sectional area of air duct

Effective cross-sectional area of air duct (Eqn F.64)

Maximum cross-sectional area of aerated flow

Total cross-sectional area of tunnel

Cross-sectional area of non-aerated flow

Amplitude of undulation; coefficients in Eqns 14, B.16, B.19

and 5.38

Coefficients in Eqn F.46

Surface width of flow, or width of channel

Coefficients in Eqns B.16 and B.39

Concentration of air

Concentration of air in terms of volumes

Concentration of air in terms of volumetric flow rates

Mean concentrations of air (depth-averaged)

Drag coefficient (with cavitation)

Drag coefficient without cavitation

Skin friction coefficient

Pressure coefficient (Eqn B.l)

Minimum pressure coefficient

Coefficients in Eqn 8.16 and F.39

Coefficients in Eqn C.l

Diameter of pipe or tunnel

Downstream diameter

Diameter of orifice

Upstream diameter

Depth of flow measured normal to bed

Depth of flow at vena contracta

Equivalent water depth for aerated flow (Eqn F.lO)

Transition depth in aerated flow

Depth of non-aerated flow

Length of transition downstream of gate slot (see Fig 5)

Euler number (Eqn F.38)

Stabilised depth of cavitation erosion

i Froude number (= v/(~A/B) )

Value of F just upstream of hydraulic jump

Value of F at vena contracta

Equivalent Froude number for aerated flow (Eqn F.13)

Value of F for start of air entrainment

Froude number based on hydraulic radius (Eqn F.20)

Froude number based on characteristic length (Eqn F.17)

Frequency of vortex shedding

Constant in Eqn F.56

Acceleration due to gravity

Total head

Static pressure head at point of incipient cavitation

Vertical distance below level of reservoir surface

Vickers Hardness of material for applied load of 5kg

Height of step, irregularity or baffle block; depth of offset

or gate slot; vertical height of ramp

Height of ramp measured normal to invert of channel

Maximum height of aerated flow

Cavitation intensity (Eqn 5)

Parameter for inception of air entrainment (Eqn F.ll)

Energy gradient of flow

Parameter for rate of decrease of air concentration (Eqn F.50)

Cavitation index

Critical value of K (corresponding to continuous but light

cavitation noise)

Incipient cavitation index (Eqn 3)

Value of K for desinent cavitation

Value of K for incipient damage

Local value of K. 1

Value of K estimated from pressure measurements i

Value of K for a rectangular gate slot i

Value of K. for a square-shaped gate slot L

Entrainment constant for aerator (Eqn F.40)

Nikuradse sand roughness

Length of irregularity or gate slot

Length of air duct

Length of air cavity produced by aerator

Horizontal distance between adjacent aerators

Distance to inception of self-aeration, measured from upstream

end of channel A.2

Compressive strength of material

Coefficient in Eqn 14

Overall head-loss factor for air duct (Eqn F.58)

Number of vortices in gate slot

Manning roughness coefficient; slope of surface relative to

incident flow (n units parallel to flow to 1 unit normal to

flow)

Total pressure

Upstream total pressure

Static pressure

Static pressure at reference point 0

Static pressure at general point 1

Critical static pressure for growth of nuclei

Downstream static pressure

Vapour pressure of liquid

Pressure difference across jet (positive if pressure on upper

surface is greater than pressure on lower surface)

Volumetric flow rate

Volumetric flow rate of air

Volumetric flow rate of water

Volumetric flow rate of water per unit width

Volumetric flow rate of air per unit width

Hydraulic radius (flow arealwetted perimeter)

Value of R for air duct

Cavitation resistance (= [rate of loss of weightlunit area l)

Reynolds number

Value of R for non-aerated flow

Radius of curvature

Radius oE bubble

External radius

Internal radius

Strouhal number (Equation C.3)

Area of opening of gate; geometric scale ratio

(prototype/model)

Incubation period for cavitation damage

Dimension at downstream end of gate slot (Fig 5); vertical

depth of groove at aerator (Fig 8)

Depth of groove at aerator measured normal to invert of

channel

Constant in Eqn E.l

O f f s e t of downstream w a l l away from f low ( F i g 5 ) ; v e r t i c a l

o f f s e t of channe l f l o o r a t a e r a t o r ( F i g 8 )

O f f s e t of channe l f l o o r a t a e r a t o r measured normal t o i n v e r t

Flow v e l o c i t y

Mean v e l o c i t y of wa te r i n a e r a t e d f low (Equa t ion F.9)

Water v e l o c i t y a t p o i n t above bed where a i r c o n c e n t r a t i o n i s

90% 1

Shear v e l o c i t y (= ( g ~ i ) ' )

Mean v e l o c i t y of a i r - w a t e r m i x t u r e

R i s e v e l o c i t y of a i r bubble

V e l o c i t y a t downstream end of a i r c a v i t y produced by a e r a t o r

Net v e l o c i t y of a i r en t ra inment

Volumet r i c r a t e of i n f l o w of a i r per u n i t s u r f a c e a r e a of

f l o w

V e l o c i t y f o r s t a r t of a i r e n t r a i n m e n t

V e l o c i t y a t r e f e r e n c e p o i n t 0

Allowable f low v e l o c i t y f o r i n c u b a t i o n p e r i o d T

Non-aerated f low v e l o c i t y

Volume; v e r t i c a l d e p t h of s l o t a t a e r a t o r ( F i g 8 )

Depth of s l o t a t a e r a t o r measured normal t o i n v e r t of c h a n n e l

Volume of a i r

Volume of wa te r

Weber number (Eqn F.18)

Weber number (Eqn F.38)

O v e r a l l s t e p h e i g h t a t a e r a t o r ( = h + t , o r h + U)

S c a l e e f f e c t ( r a t i o of p r o t o t y p e v a l u e t o model v a l u e

t r ans fo rmed a c c o r d i n g t o Froude c r i t e r i o n )

Dimensionless parameter (Eqn F.37)

D i s t a n c e measured p a r a l l e l t o s u r f a c e of channe l

D i s t a n c e measured normal t o s u r f a c e of channe l

Value of y a t which a i r c o n c e n t r a t i o n i s 90%

V e r t i c a l e l e v a t i o n of p o i n t above r e f e r e n c e l e v e l

Angle of chamfer r e l a t i v e t o i n c i d e n t f low

R a t i o of v o l u m e t r i c f low r a t e of a i r t o v o l u m e t r i c f low r a t e

of wa te r

Volume of c a v i t a t i o n e r o s i o n w i t h a i r a s p r o p o r t i o n of volume

of e r o s i o n wi thou t a i r

P r o p o r t i o n a t e change i n t ime-averaged v e l o c i t y ; t h i c k n e s s of

boundary l a y e r ; v e r t i c a l roughness i n d e x a t a e r a t o r

P r o p o r t i o n a t e f l u c t u a t i o n i n v e l o c i t y

V e l o c i t y head c o e f f i c i e n t s f o r l o s s e s i n a i r d u c t

Dimensionless parameter (Eqn B.36)

Angle of channe l t o h o r i z o n t a l

Wavelength of u n d u l a t i o n ; Darcy-Weisbach f r i c t i o n E a c t o r

(= 8gRi/V 2) F r i c t i o n Eac to r f o r a e r a t e d f l o w

F r i c t i o n Eac to r f o r non-aera ted f l o w

Kinemat ic v i s c o s i t y of l i q u i d

F a c t o r i n Eqn D . l

Dens i ty of l i q u i d

Dens i ty of a i r

S u r f a c e t e n s i o n of l i q u i d

Average s h e a r s t r e s s

Angle of ramp of a e r a t o r r e l a t i v e t o c h a n n e l

S c a l e f a c t o r i n Eqn G.3

Channel shape parameter (Eqns F.14 a , b )

APPENDIX B

CAVITATION AT SURFACE IRREGULARITIES

B.l General Most studies have been concerned with determining

values of the parameter K. (see Equations 3 and 4) for 1

incipient (or desinent) cavitation at surface

irregularities. Results have been obtained:

1. theoretically;

2. by laboratory experiments,

3. by field tests and observations.

Generally the various values of K for a particular i

type of excrescence are in reasonable agreement, but

direct comparisons between experiments are not always

possible because of different definitions of the

characteristic pressure and velocity (p and V in 0 0

Equation 3), and different means of identifying the

limit of cavitation (by eye, by sound or by increase

in turbulence levels).

B. 2 Theoretical Most results in this category apply to streamlined

studies types of irregularity for which the flow remains

attached to the surface. Values of the pressure

coefficient

along the boundary are determined theoretically,

usually by means of potential flow theory. It is then

assumed that when cavitation begins the minimum

pressure on the surface is equal to the vapour

pressure p of the liquid; thus from Equation 3 the v

inception parameter is given by

where C is t h e minimum v a l u e of t h e p r e s s u r e pm

c o e f f i c i e n t on t h e i r r e g u l a r i t y . T h i s approach

n e g l e c t s t h e e f f e c t of boundary-layer development and

t h e i n f l u e n c e of t u r b u l e n t p r e s s u r e f l u c t u a t i o n s which

w i l l t e n d t o r e s u l t i n h igher - than-pred ic ted v a l u e s of

Ki-

Rosanov e t a 1 (1965) d e s c r i b e r e s u l t s o b t a i n e d by

conformal t r a n s f o r m a t i o n f o r s t r e a m l i n e d

i r r e g u l a r i t i e s c o n s i s t i n g of c i r c u l a r a r c s (Type 7B i n

F i g u r e L). For f low w i t h a f r e e s u r f a c e , t h e c r i t i c a l

c a v i t a t i o n number was found t o be

where h i s t h e h e i g h t of t h e i r r e g u l a r i t y and L i s i t s

l e n g t h . The formula was checked e x p e r i m e n t a l l y f o r a

v a l u e of h/L = 0.38. Xu h Zhou (1982) a l s o used

conformal t r a n s f o r m a t i o n s t o c a l c u l a t e t h e minimum

p r e s s u r e c o e f f i c i e n t s f o r i r r e g u l a r i t y Types LD and 78

i n both open channe l s and p r e s s u r e c o n d u i t s . T h e o r e t i c a l and e x p e r i m e n t a l r e s u l t s were p r e s e n t e d

g r a p h i c a l l y i n t h e form

where d i s t h e d e p t h of f low.

Zhurav l iova (1983) s t u d i e d f low o v e r d i f f e r e n t t y p e s

of smoothly u n d u l a t i n g s u r f a c e , and concluded t h a t t h e

most s e v e r e case was provided by s i n u s o i d a l v a r i a t i o n s

of type

y = a s i n ( 2 m l h ) (B-5)

i n which a i s t h e ampl i tude of t h e u n d u l a t i o n and h i s

i t s wave l e n g t h . The cor respond ing v a l u e of t h e

p r e s s u r e coef f i c L e n t i s

C = - 4 m - 0 ( d l h) s i n (2 m / h) P h

where d i s t h e f low dep th ; t h e v a l u e of V used i n 0

c a l c u l a t i n g C from Equa t ion B . l is t h e u n d i s t u r b e d P

a v e r a g e v e l o c i t y upstream of t h e u n d u l a t i o n . F o r

f r ee - su r face f low

0 ( d / h) = t a n h ( 2 d l h ) (B.7a)

and f o r f low under p r e s s u r e

0 ( d l h ) = c o t h ( 2 d l h ) (B.7b)

I f t h e d e p t h of f low d > 2h, t h e minimum v a l u e of t h e

p r e s s u r e c o e f f i c i e n t is approx imate ly

Comparisons w i t h e x p e r i m e n t a l measurements showed t h a t

t h e c r i t e r i o n f o r t h e i n c e p t i o n of c a v i t a t i o n was

g i v e n by

where C i s t h e t h e o r e t i c a l l y - p r e d i c t e d v a l u e , and pm

t h e 0.05 t e rm t a k e s accoun t of t h e e f f e c t of t u r b u l e n t

p r e s s u r e f l u c t u a t i o n s .

Zhou e t a 1 (1984) used a f i n i t e e lement method t o

p r e d i c t v a l u e s of C f o r f o u r t y p e s of i r r e g u l a r i t y pm

(Types ID, 3B, 6B, 78 i n F igure 1 ) on t h e i n v e r t of a

p r e s s u r e c o n d u i t . The i r r e g u l a r i t i e s were assumed t o

have rounded edges of r a d i u s c. The r e s u l t s were

p r e s e n t e d g r a p h i c a l l y , and f o r Types 1 D and 7B were

g i v e n i n t h e form

For both t y p e s t h e magnitudes of C were f a i r l y pm

s i m i l a r , and d e c r e a s e d r a p i d l y w i t h r / h i n t h e range

r / h < 40; beyond t h i s l i m i t t h e v a l u e s were a l m o s t

independen t of r / h and v a r i e d between C = -0.6 a t pm

d / h = 6 and C = -0.2 a t d / h = 20. I n t h e c a s e o f pm

i r r e g u l a r i t y Types 38 and 6B i t was assumed t h a t t h e

r a d i u s of c u r v a t u r e r was e q u a l t o t h e h e i g h t h.

R e s u l t s were p r e s e n t e d i n t h e form

C = f n ( n , d / h ) ( B . l l ) pm

where n d e f i n e s t h e s l o p e of t h e i r r e g u l a r i t y ( n u n i t s

p a r a l l e l t o t h e f low t o 1 u n i t normal t o t h e f low).

The magni tudes of C f o r Types 38 and 6B were f a i r l y pm

s i m i l a r , and i n bo th c a s e s became a lmos t c o n s t a n t f o r

n > 30; i n t h i s range v a l u e s v a r i e d from abou t

C = -0.6 a t d / h = 5 t o C = -0.1 a t d / h = 20. pm pm

R e s u l t s were a l s o o b t a i n e d f o r groups of

i r r e g u l a r i t i e s a t d i f f e r e n t l o n g i t u d i n a l s p a c i n g s .

These v a r i o u s t h e o r e t i c a l r e s u l t s app ly t o

two-dimensional i r r e g u l a r i t i e s , and t h e v a l u e s of L/h

need t o be q u i t e l a r g e f o r t h e assumpt ion of no f l o w

s e p a r a t i o n t o be v a l i d . They a r e t h e r e f o r e not

s u i t a b l e f o r e s t i m a t i n g t h e c a v i t a t i o n p o t e n t i a l of

t y p i c a l c o n s t r u c t i o n f a u l t s , such a s t h o s e a t

mis-a l igned j o i n t s , but can be used t o d e f i n e

p e r m i s s i b l e t o l e r a n c e s f o r remedia l works.

I n t h e c a s e of s e p a r a t e d f l o w s , Johnson (1963)

sugges ted t h a t a r easonab le e s t i m a t e of t h e c a v i t a t i o n

p a r a m e t e r i s g i v e n by

where C i s t h e p r e s s u r e c o e f f i c i e n t a t t h e po in t on pm

t h e s u r f a c e a t which t h e f low s e p a r a t e s . T h i s r e s u l t

is o b t a i n e d by assuming t h a t t h e minimum p r e s s u r e i n

t h e f l u i d o c c u r s a t t h e c e n t r e of a f o r c e d v o r t e x c o r e

formed a t t h e p o i n t of s e p a r a t i o n .

B . 3 Laboratory Exper iments t o de te rmine t h e c o n d i t i o n s f o r i n c i p i e n t

atudiea c a v i t a t i o n have been c a r r i e d o u t u s i n g c a v i t a t i o n

t u n n e l s ( p r e s s u r e f low) and vacuum t e s t r i g s

( f r e e - s u r f a c e f low) , u s u a l l y w i t h t h e ambient p r e s s u r e

reduced below a tmospher ic .

B a l l (1963) p rov ided c u r v e s f o r de te rmin ing t h e l i ~ n i t

of c a v i t a t i o n f o r in to - the - f low o f f s e t s and chamfers

( i r r e g u l a r i t y t y p e s l A , 18 , l C , 3A i n F i g u r e 1 ) . The

c u r v e s a r e expressed i n d imens iona l form, and g i v e t h e

s t a t i c p r e s s u r e head H . f o r i n c i p i e n t c a v i t a t i o n a s a 1

f u n c t i o n of t h e f a l lowing v a r i a b l e s :

Type 1 A : H . = f n ( V h) 1 0'

(B. 1 3 a )

Types lB , 1 C : Hi = f n (V h , r ) 0 '

(B.13b)

Type 3A : Hi = f n (Vo, n) ( B . 1 3 ~ )

where V i s t h e a v e r a g e f low v e l o c i t y . Ana lys i s of 0

t h e g raphs s u g g e s t s t h a t t h e cor respond ing v a l u e s of

t h e c a v i t a t i o n pa ramete r K do no t vary g r e a t l y w i t h i

f low v e l o c i t y f o r a g i v e n shape and s i z e of

i r r e g u l a r i t y . However, i n t h e c a s e of t h e t h r e e Type

1 i r r e g u l a r i t i e s t h e r e i s a s t r o n g dependence of K on i

t h e h e i g h t h of t h e o f f s e t . Given t h i s behaviour , i t

i s perhaps s u r p r i s i n g t h a t t h e v a l u e s of K. f o r t h e 1

Type 3A chamfer a p p e a r t o depend on ly upon t h e s l o p e

n. Approximate v a l u e s of K f o r t h e i r r e g u l a r i t i e s i

a r e g i v e n i n Tab le 2 , b u t i t i s s t r e s s e d t h a t t h e s e

have been determined from t h e g raphs and n o t from t h e

o r i g i n a l d a t a . Fa lvey (1984) ment ions t h a t B a l l ' s

exper imen t s were c a r r i e d o u t i n a w a t e r t u n n e l

measuring 102mm h i g h by 152mm wide, and t h a t t h e

t h i c k n e s s of t h e boundary l a y e r was abou t 2mm.

Johnson (1963) g i v e s v a l u e s of Ki f o r a sharp-edged

o f f s e t away from t h e f low (Type 2A i n F i g u r e 1 ) . The

g r a p h i c a l r e s u l t s can b e d e s c r i b e d a p p r o x i m a t e l y by

where t h e d e p t h h of t h e o f f s e t is i n mm.

Rosanov e t a 1 (1965) p rov ide d a t a f o r f o u r t y p e s o f

i r r e g u l a r i t y a s f o l l o w s :

I r r e g u l a r i t y Type Ki

The v a l u e s of K were c a l c u l a t e d u s i n g t h e a v e r a g e i

f l o w v e l o c i t y i n t h e c o n t r a c t e d s e c t i o n . No ment ion

i s made of any v a r i a t i o n of K w i t h t h e h e i g h t of t h e i

i r r e g u l a r i t y . The in to - the - f low o f f s e t (Type 1A) was

a l s o t e s t e d w i t h p o s i t i v e and n e g a t i v e s l o p e s of 1 :5

and 1:10 downstream of t h e s t e p ; t h e l a r g e s t v a l u e of

Ki = 2.4 o c c u r r e d w i t h a s l o p e of 1 :10 away from t h e

f low. I n t h e c a s e of t h e o f f s e t Type 2A, v a r y i n g t h e

s l o p e ups t ream of t h e s t e p d i d n o t a l t e r K from t h e i

f i g u r e o f 1.1.

G a l p e r i n e t a 1 (1977) d e f i n e d v a l u e s of K i u s i n g t h e

u n d i s t u r b e d f low v e l o c i t y a t t h e l e v e l of t h e t o p o f

t h e i r r e g u l a r i t y and o b t a i n e d

I r r e g u l a r i t y Type Ki

It was found t h a t t h e s e v a l u e s were no t dependent o n

t h e h e i g h t h of t h e i r r e g u l a r i t y r e l a t i v e t o t h e

t h i c k n e s s 6 of t h e boundary l a y e r ( f o r h / 6 S 2 .5) .

R e s u l t s f o r a chamfer i n t o t h e f l o w (Type 3A i n F i g u r e

1 ) can be approximated by

where t h e s l o p e of t h e chamfer i s n u n i t s p a r a l l e l t o

t h e f low t o 1 u n i t normal t o t h e f low.

Arndt et a 1 (1979) a n a l y s e d d a t a f o r s i x types o f

i r r e g u l a r i t y , and found t h a t t h e v a l u e of K f o r

d e s i n e n t c a v i t a t i o n , K d , depended upon t h e Reynolds

number and upon t h e h e i g h t h of t h e excrescence

r e l a t i v e t o t h e boundary l a y e r t h i c k n e s s 6. R e s u l t s

were f i t t e d t o a n e q u a t i o n of t h e form

where V i s t h e v e l o c i t y o u t s i d e t h e boundary l a y e r . 0

The c o e f f i c i e n t s a , b and c va ry accord ing t o t h e t y p e

of i r r e g u l a r i t y a s f o l l o w s :

I r r e g u l a r i t y Type a b C

Falvey (1982) combined d a t a f o r in to-f low chamfers

(Type 3A) o b t a i n e d by Colegate (1977) and J i n e t a1

(1980) which showed t h a t

I n t h e c a s e of abrup t chamfers w i t h n 5 1, t h e v a l u e

of K depends only upon t h e h e i g h t h of t h e chamfer, i

t h i s dependency is d e s c r i b e d approximately by

where h i s i n mm. I n t h e range 1 < n < 5 , K v a r i e s i

w i t h both t h e h e i g h t and s l o p e of t h e chamfer. Fa lvey

ment ions t h a t t h e d a t a were ob ta ined wi th v i r t u a l l y no

boundary l a y e r , s o t h e l i m i t i n g v e l o c i t y cor responding

t o K i s t h e l o c a l v a l u e a t t h e l e v e l of t h e i

i r r e g u l a r i t y . These r e s u l t s a r e i n reasonab le

agreement w i t h those of G a l p e r i n e t a 1 ( s e e Equa t ions

B.15a. b).

K e l l e r 6 Koch (1982) s t u d i e d c a v i t a t i o n c o n d i t i o n s f o r

a s q u a r e block mounted on t h e f l o o r of a r e c t a n g u l a r

channe l and s u b j e c t t o s u p e r c r i t i c a l f r e e - s u r f a c e

f lows . The r a t i o of t h e block h e i g h t t o t h e upst ream

wate r d e p t h was kep t c o n s t a n t a t 0.142. A t Froude

numbers of F < 2, i t was found t h a t i n c r e a s i n g t h e

amount of t u r b u l e n c e i n t h e flow i n c r e a s e d t h e v a l u e

of K ; f o r F > 2, t h e r e s u l t s were l i t t l e a f f e c t e d i'

by t h e d e g r e e of tu rbu lence . The v a l u e s of Ki reached

a maximum of K = 2.6 a t F = 2.11, and then decreased i

t o Ki = 2.0 a t F = 3.24. This i n d i c a t e s t h a t

c a v i t a t i o n c h a r a c t e r i s t i c s may be modif ied i f

i r r e g u l a r i t i e s a r e l a r g e enough t o cause a n

i n t e r a c t i o n w i t h t h e Free s u r f a c e .

L iu (1983) found t h a t v a l u e s of K f o r t h r e e t y p e s of i

i r r e g u l a r i t y could be d e s c r i b e d by a n e q u a t i o n of t h e

form

where t h e h e i g h t of t h e i r r e g u l a r i t y i s i n mm, and t h e

c o n s t a n t a h a s t h e fo l lowing v a l u e s :

I r r e g u l a r i t y Type a

The h e i g h t s of t h e i r r e g u l a r i t i e s s t u d i e d i n t h e tests

v a r i e d between l m m and 15mm. R e s u l t s were a l s o

o b t a i n e d f o r i n t o - f l o w chamfers (Type 3A) f o r which

Ki = 2.9 .-'m'6 , f o r 2 S n S 12 (B.20)

The chamfers t e s t e d a l l had a h e i g h t of h = l h m .

Kudriashov e t a 1 (1983) i n v e s t i g a t e d t h e i n c e p t i o n of

c a v i t a t i o n a t changes i n channe l s l o p e away from t h e

f low ( i r r e g u l a r i t y t y p e 4B). R e s u l t s f o r t h r e e

d e f l e c t i o n a n g l e s were

Exper iments on chamfers angled away from t h e f low

( i r r e g u l a r i t y t y p e 4A) were a l s o c a r r i e d o u t by

Demir'dz & Acatay (1985). F o r d e f l e c t i o n a n g l e s of a

20° , t h e f low remained a tcached t o t h e boundary, and

p r e s s u r e s were measured by s u r f a c e t a p p i n g s . A t

l a r g e r d e f l e c t i o n a n g l e s t h e f low s e p a r a t e d , and

p r e s s u r e s were c a l c u l a t e d From measurements of

v e l o c i t y w i t h i n t h e f l u i d o b t a i n e d u s i n g a

Laser-Doppler anemometer. For non-separa t ing f lows ,

t h e measured v a l u e s of K . were independent of t h e 1

d e p t h of t h e chamfer and f i t t e d t h e e q u a t i o n

Ki = 0.16 + 0.015 a , f o r 10" ,< a 5 20' (B.21)

where t h e a n g l e a i s i n d e g r e e s . When t h e f l o w

s e p a r a t e d , K. was a lmos t independent of a b u t v a r i e d 1

w i t h t h e d e p t h h of t h e chamfer

Value of Ki a = 25" a = 90"

For a n g l e s between 20' < a < 25'. K depended upon i

bo th a and h. These v a l u e s of K . a r e lower than t h o s e 1

o b t a i n e d by Kudriashov e t a 1 (1983) who determined t h e

o n s e t of c a v i t a t i o n d i r e c t l y .

Scheur (1985) determined t h e c o n d i t i o n s f o r i n c i p i e n t

c a v i t a t i o n f o r f i v e t y p e s of i r r e g u l a r i t y w i t h h e i g h t s

v a r y i n g between 5mm and 20mm. The v a l u e s of Ki

o b t a i n e d a t a f r e e s t r e a m v e l o c i t y of 8mIs f o r

i r r e g u l a r i t i e s of h e i g h t h = l0mm were

I r r e g u l a r i t y t y p e ( K i ) 10

Values of K i f o r o t h e r h e i g h t s were r e l a t e d t o t h o s e

f o r h = lOmm by t h e fo l lowing f a c t o r s

Height h (mm)

The r e s u l t s f o r t h e r e c t a n g u l a r r i b (Type 5A) were

a l s o e x p r e s s e d i n t h e form

This e q u a t i o n i s s i m i l a r i n t y p e t o t h e one used by

Arndt e t a 1 (1979) ( s e e Equa t ion B.16), but t h e

c o e f f i c i e n t s have s i g n i f i c a n t l y d i f f e r e n t v a l u e s .

Exper imenta l d a t a f o r in to - f low chamfers (Type 3A)

were p r e s e n t e d by Novikova h Semenkov (1985). The

v a l u e s of K were c a l c u l a t e d u s i n g t h e v e l o c i t y a t t h e i

l e v e l of t h e t o p of t h e chamfer , and were r e p r e s e n t e d

by t h e f o l l o w i n g e q u a t i o n s

-0.7 Ki = 2.311 , f o r n > 1

Ki = 2.3 , f o r n S 1

(8.23)

( H . 24)

These v a l u e s a r e h i g h e r than t h o s e found by G a l p e r i n

e t a 1 (1977) and Falvey (1982) . a l t h o u g h i t i s

noteworthy t h a t t h e exponent of n i n E q u a t i o n B.23 i s

t h e same a s i n F a l v e y ' s Equa t ion B.17.

The i n f o r m a t i o n g i v e n s o f a r a p p l i e s t o

two-dimensional i r r e g u l a r i t i e s . Zharov h Kudryashov

(1977) t e s t e d th ree -d imens iona l i r r e g u l a r i t i e s of Type

3C ( s e e F i g u r e 1 ) both s i n g l y and i n g roups . The

h e i g h t h of t h e e x c r e s c e n c e s was v a r i e d from 3mm t o

10mm, and t h e chamfer a n g l e a from 15' t o 90" (where n

= c o t a ) . A l l t h e r e s u l t s were w e l l d e s c r i b e d by t h e

formula

Ki = 2.0 s i n a (B.25)

w i t h no dependence on h. The c h a r a c t e r i s t i c v e l o c i t y

was t aken a s t h a t a t h e i g h t h i n t h e absence of t h e

p r o j e c t i o n .

I f a n i r r e g u l a r i t y does n o t p r o j e c t o u t s i d e t h e

boundary l a y e r , t h e v e l o c i t y V a t t h e l e v e l of t h e t i p

of t h e e x c r e s c e n c e i s g iven a c c o r d i n g t o G a l p e r i n e t

a 1 (1977) by

where k i s t h e Nikuradse sand roughness , and where S

t h e s h e a r v e l o c i t y V* i s r e l a t e d t o t h e s h e a r s t r e s s

z a t t h e s u r f a c e by 0

T u r b u l e n t p r e s s u r e f l u c t u a t i o n s i n a boundary l a y e r

c a n c a u s e c a v i t a t i o n t o occur on p l a n e s u r f a c e s .

Arndt e t a 1 (1979) found ( f o r d e s i n e n t c a v i t a t i o n )

t h a t

where t h e s k i n f r i c t i o n c o e f f i c i e n t C is d e f i n e d by f

For rough- tu rbu len t f low over a p l a n e s u r f a c e , t h e

v a l u e of C a t a d i s t a n c e X from t h e s t a r t of t h e f

boundary l a y e r can be e s t i m a t e d from

An a l t e r n a t i v e formula f o r de te rmin ing t h e s k i n

f r i c t i o n c o e f f i c i e n t is g iven by Duncan e t a 1 (1962,

p330) a s

C a v i t a t i o n can a l s o be produced when t h e r e i s a

sudden change i n s u r f a c e roughness , a s f o r example a t

t h e end of a s e c t i o n of c o n c r e t e channel p r o t e c t e d by

a steel l i n i n g . According t o Kudriashov et a 1 (1983).

i f t h e downstream roughness h e i g h t k 2 i s much g r e a t e r

t h a n t h e upst ream v a l u e k l , t h e n t h e c a v i t a t i o n

p o t e n t i a l of t h e d i s c o n t i n u i t y i s e q u i v a l e n t t o a n

in to - f low chamfer of h e i g h t k 2 and s l o p e n = 10.

A l l t h e r e s u l t s d e s c r i b e d s o f a r a p p l y t o uniform

f lows o v e r i r r e g u l a r i t i e s on p l a n e s u r f a c e s . Values

of t h e c a v i t a t i o n pa ramete r f o r non-uniform c o n d i t i o n s

can be c a l c u l a t e d by means of t h e s o - c a l l e d " a d d i t i o n

theorem" d e s c r i b e d by Arndt e t a 1 (1979). Le t Ki l be

t h e l o c a l v a l u e of t h e i n c i p i e n t c a v i t a t i o n index f o r

a n i r r e g u l a r i t y on a p l a n e s u r f a c e . Now l e t t h e

i r r e g u l a r i t y be p l a c e d a t a p o i n t where t h e l o c a l

p r e s s u r e and v e l o c i t y ( p , V) a r e d i f f e r e n t from t h e

f ree-s t ream v a l u e s (p Vo); t h e p r e s s u r e c o e f f i c i e n t 0'

C f o r t h e p o i n t can be c a l c u l a t e d from E q u a t i o n P

( B . ) . It can t h e n be shown from B e r n o u l l i ' s e q u a t i o n

t h a t t h e c a v i t a t i o n index f o r t h e i r r e g u l a r i t y ,

d e f i n e d i n terms of f r ee - s t ream c o n d i t i o n s , i s g i v e n

by

The v a l i d i t y of t h i s r e s u l t has been checked

e x p e r i m e n t a l l y .

L i (1982) d e s c r i b e s a method f o r d e s i g n i n g t h e

s e c t i o n a l p r o f i l e of a s p i l l w a y s o a s t o reduce o r

eliminate the possibility of cavitation. Suitable

profiles are obtained by varying the radius of

curvature so as to maintain a constant value of the

cavitation index K (Equation 2) along the surface of

the spillway, alternatively the profile may be

selected so as to keep the pressure at the bed

constant.

The presence of sediment in water influences the

occurrence of cavitation. Liu (1983) carried out

experiments with a circular cylinder to determine how

the limit of incipient cavitation varied with sediment

concentration. For concentrations up to 10kg/m3, the

values of K were slightly higher than for clear i

water; increasing the concentration from 10kg/m to

70kg/m3 decreased K, to about 80% of its clear-water l

value; above 70kg/m3 the values of K. remained 1

approximately constant. Research reported by Lin et

a1 (1987) also showed that sediment accelerated the

rate of cavitation pitting, but did not alter the

final depth of erosion.

It is convenient to include in this section

experimental information about cavitation at bends in

circular pipes. Kudriashov et a1 (1983) found that

measurements of incipient cavitation fitted the

formula

where K. and r are respectively the internal and L e

external radii of curvature of the pipe.

Tullis (1981) studied cavitation in 90' bends with

nominal diameters of 75, 150 and 300mm. Flow

conditions were determined for incipient cavitation

(light and intermittent noise) and critical cavitation

( c o n t i n u o u s bu t l i g h t n o i s e ) . The c r i t i c a l c a v i t a t i o n

c r i t e r i o n was recommended f o r d e s i g n a s i t cor responds

t o t h e p o i n t beyond which p i t t i n g of t h e p i p e s u r f a c e

begins . Pipe s i z e was found t o have a s i g n i f i c a n t

e f f e c t on t h e v a l u e s of t h e c a v i t a t i o n pa ramete r s .

The r e s u l t s f o r i n c i p i e n t and c r i t i c a l c o n d i t i o n s were

d e s c r i b e d r e s p e c t i v e l y by

where t h e p i p e d i a m e t e r D i s i n mm; t h e v a l u e of

p r e s s u r e used t o c a l c u l a t e K and K from E q u a t i o n 2 i C

was t h e t o t a l p r e s s u r e upst ream of t h e bend ( s t a t i c

p l u s v e l o c i t y head) . Although t h i s work i s n o t

s t r i c t l y r e l e v a n t t o c o n d i t i o n s i n t u n n e l s p i l l w a y s ,

i t does i n d i c a t e t h a t models of such s t r u c t u r e s may be

s u b j e c t t o i m p o r t a n t s c a l e e f f e c t s .

B.4 F i e l d s t u d i e s Most f i e l d d a t a concern ing a l l o w a b l e i r r e g u l a r i t i e s on

p r o t o t y p e s t r u c t u r e s have been o b t a i n e d from s u r v e y s

c a r r i e d o u t a f t e r c a v i t a t i o n damage had o c c u r r e d .

However, two s y s t e m a t i c s t u d i e s a t f u l l s c a l e have

been made t o s t u d y t h e o n s e t and development of

c a v i t a t i o n , and t h e s e a r e d e s c r i b e d a t t h e end of t h i s

s e c t i o n .

Wagner (1967) d e s c r i b e s c a v i t a t i o n damage downstream

of g a t e s i n t h e d i v e r s i o n t u n n e l of Glen Canyon Dam

(USA). The g a t e s were used t o c o n t r o l f lows w i t h

heads of up t o a b o u t 102m. Eros ion due t o c a v i t a t i o n

was found a t t h e f o l l o w i n g p l a c e s :

l. minor i r r e g u l a r i t i e s i n t h e s t e e l l i n e r

f i t t e d downstream of t h e g a t e s caused damage

t o a maximum d e p t h of 10mm;

2. i r r e g u l a r i t i e s i n a p p l i c a t i o n of p a i n t

c o a t i n g ;

3. o f f s e t s i n t o t h e f low of more t h a n 0.8mm

caused c a v i t a t i o n a t Flow v e l o c i t i e s of

41mIs.

S u r f a c e d e p r e s s i o n s of l e s s t h a n 3mm d i d no t l e a d t o

damage; d e p r e s s i o n s of 6mm r e s u l t e d i n some removal

of t h e p a i n t c o a t i n g and minor p i t t i n g .

G a l p e r i n e t a 1 (1977) g i v e d e t a i l s of c a v i t a t i o n

damage which occur red a t s e v e r a l l a r g e dams. Supkhun

Dam (Korea) h a s a s p i l l w a y s l o p e of 1:0.78 and a n

o v e r a l l head of abou t l o b , and was des igned f o r u n i t

d i s c h a r g e s of up t o 64m3/s/m. C a v i t a t i o n damage

occur red d u r i n g t h e f i r s t o p e r a t i n g season and

o r i g i n a t e d a t h o r i z o n t a l c o n s t r u c t i o n j o i n t s ; 200

c a v i t i e s w i t h d e p t h s exceeding O . l m were n o t e d , and

t h e t o t a l volume of e r o s i o n was l l 0 h 3 . A f t e r twelve

y e a r s of s e r v i c e t h e volume had i n c r e a s e d t o 10,000m3,

and t h e maximum d e p t h of e r o s i o n was 2.4m.

The s p i l l w a y of B r a t s k Danm (USSR) has a s l o p e of

1 :0 .8 and a n o v e r a l l head of 95m, and a t normal

r e s e r v o i r l e v e l t h e u n i t d i s c h a r g e i s 30.5m3/s/m. The

s t r e n g t h of t h e c o n c r e t e v a r i e d between 34MPa and

54MPa w i t h a n average of 44MPa. I m p e r f e c t i o n s i n

s u r f a c e f i n i s h found a f t e r c o n s t r u c t i o n inc luded

s t epped d rops of up t o 80mm due t o d i sp lacement of

formwork, u n d u l a t i o n s , and i s o l a t e d i r r e g u l a r i t i e s

such a s h o l e s and lumps of c o n c r e t e . C a v i t a t i o n

e r o s i o n occur red f i r s t a t t h e l a r g e s t i r r e g u l a r i t i e s

s u b j e c t e d t o t h e h i g h e s t v e l o c i t i e s . The b i g g e s t h o l e

was downstream of a 60-80mm h igh p r o j e c t i o n , and

measured 7.5m wide by 10.5m long w i t h a maximum d e p ~ h

of 1.2m. The maximum r a t e of e r o s i o n observed was

18mmlday. C a v i t a t i o n damage a l s o o r i g i n a t e d a t d e s i g n

f e a t u r e s such a s d r a i n h o l e s .

The c o n s t r u c t i o n of Krasnoyarsk Dam (USSR) b e n e f i t e d

from t h e e x p e r i e n c e o b t a i n e d a t B r a t s k . The s p i l l w a y

h a s a s l o p e of 1:0.8, a n o v e r a l l head of abou t 82m,

and a u n i t d i s c h a r g e of 59m3/s/m a t normal r e s e r v o i r

l e v e l ; t h e s t r e n g t h of t h e c o n c r e t e was 52-53MPa. An

improved s u r f a c e f i n i s h was o b t a i n e d by changes i n t h e

d e s i g n of t h e formwork, and remaining s u r f a c e

i m p e r f e c t i o n s were ground t o chamfers w i t h s l o p e s of

between 1 : 5 and 1:13. D e s p i t e t h e s e p r e c a u t i o n s , some

c a v i t a t i o n damage d i d s t i l l o c c u r , bu t i t was less

s e v e r e t h a n a t B r a t s k , w i t h t h e maximum r a t e of

e r o s i o n being reduced t o lmm/day.

Lowe e t a 1 (1979) document c a v i t a t i o n damage which

o c c u r r e d a t T a r b e l a Dam ( P a k i s t a n ) on c h u t e s

downstream of two t u n n e l s (Nos 3 and 4) c o n t r o l l e d by

r a d i a l g a t e s . The p r o f i l e s of t h e c h u t e s were

des igned t o g i v e approx imate ly a t m o s p h e r i c p r e s s u r e on

t h e lower s u r f a c e s . Causes of t h e c a v i t a t i o n were:

1. p a t c h e s of m o r t a r l e f t by m i s t a k e : a f t e r

r e p a i r w i t h o r d i n a r y c o n c r e t e , no f u r t h e r

damage o c c u r r e d ;

2. i r r e g u l a r i t i e s i n t h e f l o o r : s t e p s of

1.6-2.4mm a t t r a n s i t i o n from s t e e l t o

c o n c r e t e s u r f a c e , and 3mm h i g h humps w i t h

s l o p e changes of abou t 1 :20 ;

3. j o i n t s des igned w i t h o f f s e t s away from t h e

f low of 13-19mm, and d o u b l e c r a c k s a t

c o n t r o l j o i n t s .

The damage due t o i t e m 2 s t a r t e d a t v e l o c i t i e s o f

abou t 47-49m/s, i n d i c a t i n g v a l u e s of K f o r i n c i p i e n t

damage of approximately K = 0.08. T h i s s u g g e s t s i d

t h a t use of B a l l ' s l a b o r a t o r y d a t a ( s e e S e c t i o n B . 3

and Table 2) f o r d e s i g n w i l l e r r on t h e c o n s e r v a t i v e

s i d e . I n i t em 3 t h e c o n s t r u c t i o n of t h e j o i n t s was

changed and t h e o f f s e t s e l i m i n a t e d .

Aksoy C Ethembabaoglu (1979) g i v e d e t a i l s of

c a v i t a t i o n problems i n t h e s p i l l w a y channe l s of Keban

Dam (Turkey). Damage occurred a t i n c o r r e c t l y

cons t m c t e d t r a n s v e r s e j o i n t s which had o f f s e t s away

from t h e f low of up t o 50mm; t h e d e s i g n va lue of u n i t

d i s c h a r g e was 14.5m3/s/m width of channel and t h e

t o t a l head was abou t 120m. No damage took p l a c e i n

reg ions where t h e r e was ful ly-developed a i r

e n t r a i m e n t .

The mechanism by which a s e r i e s of c a v i t a t i o n h o l e s

forms downstream of a s t e p was d e s c r i b e d by Vorobiyov

(1983). Based on p r o t o t y p e measurements, a r a t h e r

complex e m p i r i c a l e q u a t i o n was o b t a i n e d f o r p r e d i c t i n g

t h e r a t e of l o s s of m a t e r i a l from t h e f i r s t h o l e , a n d

then from t h e subsequent ones; a s t h e h o l e s d e v e l o p ,

those downstream can e v e n t u a l l y become l a r g e r than t h e

one a d j a c e n t t o t h e s t e p . The e m p i r i c a l e q u a t i o n was

a l s o used t o s c a l e r e s u l t s from model t o p r o t o t y p e .

The f o l l o w i n g recommendations were made f o r t h e

maximum volume of e r o s i o n t h a t should be a l lowed

behind each s t e p f o r va ry ing t h i c k n e s s e s of l i n i n g :

Lining t h i c k n e s s (m) Allowable e r o s i o n (m 3,

The f i g u r e s a r e n o t r e l a t e d t o t h e t r a n s v e r s e width of

t h e s t e p , but a r e a p p a r e n t l y based on measurements of

e r o s i o n caused by t y p i c a l types of i m p e r f e c t i o n t h a t

o c c u r on p r o t o t y p e s u r f a c e s .

Falvey (1983) collected data on cavitation at seven

major dams, and observed that the incidence of damage

depended both on the value of the cavitation parameter

K and on the length of time that the structure was

operated under these conditions. Results were

presented in graphical form and are reproduced in

Figure 2; two curves are given which delimit regions

in which no damage, minor damage or major damage can

be expected. The following suggestions were also made

on the precautions which should be taken according to

the value of K occurring on a hydraulic structure:

Value of K Precaution

1.8 4 K No surface protection needed

0.25 S K 1.8 Treat surfaces (eg by grinding irregularities to flat chamfers)

0.17 S K c 0.25 Modify design (eg increase pressures by decreasing amount of curvature)

0.12 ,<K < 0.17 Add aerators (for K 0.25 if design cannot be modified)

K < 0.12 Abandon design

Cassidy h Elder (1984) cite the results of a survey

carried out by ICOLD (1980). Out of 71 large dams

operating for more than 100 days, 52 suffered no

damage, 9 slight erosion ( < 20mm depth), 2 moderate

erosion (20mm to 100mm), and 8 serious erosion (from

lOOmm to several metres). Flow velocity was the

parameter that showed the strongest correlation with

damage: of 12 chute or tunnel spillways operating at

more than 30m/s, five suffered serious erosion and

four slight or moderate erosion. Discharge per unit

width was a less reliable indicator, but the risk of

damage did appear to increase when q > 50m 3/s/m. Nany

of the problems were caused by construction faults (eg

joints and projecting reinforcement), and most were

s u c c e s s f u l l y r e p a i r e d us ing f i b r o u s o r epoxy c o n c r e t e .

Out of n i n e s p i l l w a y s equipped w i t h a e r a t o r s ( s e e

S e c t i o n F . 3 ) . s i x s t i l l s u f f e r e d c a v i t a t i o n damage

(two s e r i o u s l y ) . I n o r d e r t o c a l c u l a t e c a v i t a t i o n

p a r a m e t e r s , i t i s necessa ry t o e s t i m a t e t h e s u r f a c e

roughness of t h e s p i l l w a y s u r f a c e ; t h e b e s t c o n c r e t e

f i n i s h t h a t can be ob ta ined wi thou t s t e e l t r o w e l i n g i s

probably i n t h e range of 0.8mm t o l . l m m .

According t o Zhang (1984) . c a v i t a t i o n damage on c h u t e

s p i l l w a y s i s mostly l i k e l y a t t h e t o e where t h e

v e r t i c a l t r a n s i t i o n curve ends . Th is i s t h e r e g i o n

where t h e boundary s h e a r s t r e s s t e n d s t o be a maximum,

and where i r r e g u l a r i t i e s a r e presumably most exposed

t o l o c a l h igh v e l o c i t y f lows. T h i s argument does no t

t a k e account of s e l f - a e r a t i o n e f f e c t s which can

p reven t c a v i t a t i o n damage n e a r t h e bottom of chu te

s p i l l w a y s . Zhang c o r r e l a t e d model and p r o t o t y p e d a t a ,

and concluded t h a t t h e wors t c o n d i t i o n s f o r c a v i t a t i o n

o c c u r when t h e f o l l o w i n g parameter has t h e v a l u e

where q i s t h e u n i t d i s c h a r g e , g t h e a c c e l e r a t i o n d u e

t o g r a v i t y , and H t h e h e i g h t of t h e r e s e r v o i r s u r f a c e S

above t h e p o i n t i n q u e s t i o n .

There would no t a p p e a r t o be any fundamental r eason

why t h e p o t e n t i a l f o r c a v i t a t i o n should be g r e a t e s t

when t h e pa ramete r 11 has a c e r t a i n v a l u e . However i f

one c o n s i d e r s , f o r a p a r t i c u l a r s p i l l w a y , t h e

c o n d i t i o n s which produce t h e maximum v e l o c i t y i n t h e

v i c i n i t y of a s u r f a c e i r r e g u l a r i t y , then i t can be

s e e n t h a t t h e e f f e c t s of H and q a r e i n t e r r e l a t e d i n S

a r a t h e r complex way. A s one moves down t h e s p i l l w a y ,

t h e head H and t h e r e f o r e t h e average f low v e l o c i t y S

increase, but the boundary layer also thickens;

therefore the maximum velocity at an irregularity may

occur at some intermediate point on the spillway. As

the unit discharge q increases, the distance needed

for the boundary layer to become fully developed also

increases. Therefore, it is possible to envisage that

cavitation conditions could be most severe when a

parameter containing q and H has a certain value; the S

value of the parameter would be determined by

additional factors such as the shape of the spillway,

its surface roughness, and the type of irregularity.

As mentioned at the beginning of this Section, two

systematic studies of cavitation on spillways have

been carried out at full scale. Galperin et a1 (1977)

and Oskolkov 6 Srmenkov (1979) describe results of

field tests using "indicators" of various heights and

slopes (equivalent to irregularity types 3A and 4A in

Figure 1) placed on the surface of a spillway. Such

indicators may be made of the same materials as the

surface, or from a softer material so as to accelerate

the tests. The conditions for incipient cavitation

may be identified by the removal of a thin film of

easily-erodible material applied to the surface of the

indicator. Controlled discharges are then used to

determine the height and slope of irregularity which

will cause incipient cavitation (K.) or incipient 1

cavitation damage (K . Figure 3 is based on tests id

at Bratsk Dam (USSR), and shows how the value of Kid,

for the start of cavitation erosion, varies with the

slope of the chamfer. Perhaps surpisingly, the

chamfers angled away from the flow have slightly

higher values of K than those directed towards the id

flow.

The second systematic study was carried out by Wang 6

Chou (1979) who obtained comprehensive field data from

measurements on Feng Man, Zhe Xi and Liu Jia Xia Dams

(China); the first two have chute spillways and the

third a tunnel spillway. Between 1953 and 1975 the

Feng Man spillway operated nine times, and on each

occasion some cavitation damage occurred ; the overall

head above the toe of the spillway reached about 68m,

and the maximum unit discharge was 69m3/s/m.

Cavitation originated at faults at transverse

construction joints, which took the form of sloping

offsets and triangular-shaped irregularities (Types 3B

and 6B in Figure 1). The largest area of damage

measured 35m2, and the maximum depth of erosion was

1.21~. In 1963 and 1964 tests were carried out in

which symmetrical triangular concrete blocks of

various heights (up to 100mm) and slopes (n = 5 to 20)

were mounted on the spillway, and the resulting

cavitation damage noted Measurements of pressure at

the apex of each block showed that no erosion took

place until the time-averaged pressure fell to -7m of

water head below atmospheric, and that erosion

occurred rapidly once the pressure dropped to -9.7m.

The double amplitude of the pressure fluctuations at

an offset away from the flow was found to be 10.7% of

the average velocity head.

Wang 6 Chou provide detailed profiles of the

irregularities and the resulting cavitation holes that

occurred at the three dams. Based on these

observations, the following empirical equation was

derived for predicting the stabilised depth of

cavitation erosion

where e is the depth in mm, V is the flow velocity in 0

m/s at the level of the irregularity, and the

constants a and b are given by

(B. 38)

(B. 39)

I is a measure of the intensity of cavitation, as

defined in Equation 5. Equation B.37 is based on data

for concrete with a compressive strength of about

20-25MPa. On Feng Man Dam the time for the erosion to

reach an equilibrium depth was about 200 hours. In

order to calculate values of I in the prototype, it

was necessary to make estimates of the inception

parameter K . Tests on a 1:30 scale model were i

therefore carried out to determine the minimum

pressures at chamfers and triangular irregularities

(Types 3A and 6A in Figure 1). The results shown in

Figure 4 were then obtained by assuming K. = -C (see 1 Pm

Section B.2), and allowing for pressure fluctuations

of f 5 X of the velocity head. Comparison with Ball's

data for chamfers (see above) showed good agreement

provided K.was defined in terms of the velocity at the 1

level of the irregularity.

Wang & Chou suggest that it is unreasonable to use K. 1

as a design parameter for hydraulic structures,

because it is usually possible to accept a limited

amount of surface damage. They therefore propose that

design be based on a value of I = 0.2 (ie K = 0.8K ); i

Equation B.37 then gives

where again e is in mm and V in m/s. 0

APPENDIX C

TUNNELS AND GATES

C.l Tunnel i n l e t s Sub-atmospheric p r e s s u r e s can o c c u r a t i n l e t s t o

t u n n e l s due t o

1. convergence of t h e f l o w

2. c u r v a t u r e of t h e boundar ies

3. t u r b u l e n t p r e s s u r e f l u c t u a t i o n s i n t h e boundary

l a y e r s

4. f low s e p a r a t i o n

I n t u n n e l s w i t h h i g h - v e l o c i t y f l o w s t h e p r e s s u r e s may

become low enough t o cause c a v i t a t i o n and damage t o

t h e w a l l s . S u r f a c e i r r e g u l a r i t i e s a l s o a r e

p a r t i c u l a r l y l i a b l e t o cause c a v i t a t i o n e r o s i o n i n

s e c t i o n s of t u n n e l downstream of v e r t i c a l bends.

G a l p e r i n e t a 1 (1977) d e s c r i b e damage which o c c u r r e d

a t t h e i n t a k e s t o t h e bottom s l u i c e s of B r a t s k Dam

(USSR). Subsequent c a l c u l a t i o n s showed t h a t t h e mean

p r e s s u r e s a l o n g t h e w a l l s of t h e i n l e t s would have

been low enough t o produce c a v i t a t i o n , even wi thou t

t a k i n g t h e e f f e c t of t u r b u l e n t f l u c t u a t i o n s i n t o

a c c o u n t . However, p r e d i c t e d p r e s s u r e d i s t r i b u t i o n s o r

p r e s s u r e measurements i n models can be m i s l e a d i n g i f

t h e f low s e p a r a t e s , because t h e lowes t p r e s s u r e s w i l l

o c c u r away from t h e boundar ies .

Yan e t a 1 (1982) c a r r i e d ou t model t e s t s t o d e t e r m i n e

t h e causes of c a v i t a t i o n damage a t t h e i n l e t t o a

s h o r t s p i l l w a y t u n n e l . Downstream c o n d i t i o n s caused

t h e t u n n e l t o f low f u l l , and f low s e p a r a t i o n i n t h e

i n l e t was found t o occur due t o i t s unfavourab le

geometry and t o jets i s s u i n g from g a t e s h a f t s i n t h e

roof of t h e t u n n e l .

Hsu h Zhao (1982 ) used the technique of conformal

transformation to calculate the pressure distribution

in two-dimensional inlets having level inverts and

converging roofs of circular or elliptical shape. The

results were found to agree with experimental

measurements except in those regions where flow

separation occurred.

Zhu et a1 ( 1 9 8 2 ) used the relaxation method to

determine pressure variations in square tunnels having

axisymmetric circular inlets. The values of pressure

coefficient agreed satisfactorily with experimental

data. Tests were also carried out to determine

pressure distributions and head losses for rectangular

inlets with a level invert and converging side walls

and roof of elliptical section.

C.2 Prototype data Cavitation is a recognised danger at high-head gates

on gates such as those which are used to control flows in

low-level outlet tunnels in dams. The cavities are

often formed at points where the flow separates from a

boundary, such as at the lip of a gate or at the

corners of a slot. If a gate is partially submerged

on the downstream side, cavitation can occur in the

intense shear layer formed between the high-velocity

jet and the more static water above it. The cavities

generated at a gate may not collapse and cause damage

until they have been carried some distance downstream

by the flow. Also surface irregularities on tunnel

walls just downstream of gates are particularly liable

to cause cavitation because the boundary layers have

not developed sufficiently to protect the

irregularities from high local velocities.

Significant improvements in performance can often be

obtained by quite small changes in the configuration

of a gate or its slot, but these details usually need

t o be s t u d i e d i n a model. S t a i n l e s s s t e e l l i n i n g s a r e

sometimes used downstream of g a t e s t o p r o t e c t c o n c r e t e

s u r f a c e s from c a v i t a t i o n damage. Due t o t h e h igh c o s t

of such l i n i n g s , i t is necessa ry t o keep t h e i r l e n g t h

as s h o r t as p o s s i b l e . However, steel i s not immune

from c a v i t a t i o n damage, and problems can be caused by

i n a d e q u a t e f i x i n g and by t h e sudden change i n s u r f a c e

f i n i s h a t t h e downstream end of t h e l i n i n g .

Some examples w i l l now be g i v e n of c a v i t a t i o n damage

i n p r o t o t y p e i n s t a l l a t i o n s . Destenay h Bernard (1968)

p r o v i d e a n i n t e r e s t i n g su rvey of French e x p e r i e n c e .

Of 400 h y d r o - e l e c t r i c schemes, 21 s u f f e r e d some

e r o s i o n due t o c a v i t a t i o n . These s t r u c t u r e s tended t o

be t h o s e which had o p e r a t e d a t h igh f l o w s f o r long

p e r i o d s . T h i s f i g u r e of 2 1 i n c l u d e d one s u r f a c e

s p i l l w a y , one mid- level o u t l e t and two bottom o u t l e t s .

Four c a s e s were caused by c a v i t a t i o n a t g a t e s l o t s :

t h e e r o s i o n was f a i r l y l o c a l i s e d and i t s d e p t h was

t y p i c a l l y 100mm. The most s e r i o u s damage o c c u r r e d i n

t h e bottom o u t l e t of Serre-Poncon Dam ( F r a n c e ) . The

t u n n e l was p r o t e c t e d by a 20mm t h i c k s t e e l l i n i n g f o r

a d i s t a n c e of 15m downstream of t h e c o n t r o l g a t e .

A f t e r o p e r a t i n g a t heads of up t o 85m, a h o l e formed

10m downstream of t h e end of t h e l i n i n g , and reached a

dep th of 4m w i t h a volume of 360m3. The c a v i t a t i o n

may have been caused by t h e t r a n s i t i o n i n t u n n e l shape

from r e c t a n g u l a r t o c i r c u l a r . The damage was

r e p a i r e d , but a f t e r f u r t h e r o p e r a t i o n a t heads of up

t o 105m, a new h o l e 2m deep formed c l o s e t o t h e end of

t h e s t e e l l i n i n g . Some damage of t h e l i n i n g was a l s o

caused by c a v i t a t i o n a t t h e g a t e s l o t .

Schmi t t (1971) d e s c r i b e s problems a t Kinzua and Nadden

Dams (USA) which occur red downstream of g a t e s l o t s

n e a r t h e e n t r a n c e s t o t h e low-level t u n n e l s .

C a v i t a t i o n was caused by a n i n t e r a c t i o n between t h e

f low i n t h e t u n n e l and a h i g h - v e l o c i t y jet t r a v e l l i n g

down t h e v e r t i c a l g a t e s h a f t , which was open a t i t s

t o p end t o t h e r e s e r v o i r . The problem was so lved by

p r e v e n t i n g f low down t h e s h a f t .

Vinnogg (1971) p r o v i d e s d e t a i l s of two t u n n e l s i n

Norway which were damaged by c a v i t a t i o n . The c o n t r o l

g a t e s were o p e r a t e d 113- and 213-open f o r more than 60

d a y s i n each c o n d i t i o n . C a v i t a t i o n o r i g i n a t e d a t t h e

g a t e s l o t s and caused e r o s i o n , which i n t u r n l e d t o

worse damage f u r t h e r downstream.

G a l p e r i n e t a 1 (1977) g i v e examples of s e r i o u s

c a v i t a t i o n damage which i l l u s t r a t e t h e wide range of

p o s s i b l e c a u s e s . For g a t e d s t r u c t u r e s , t h e s e

i n c l u d e d : i n a d e q u a t e s u r f a c e smoothness of w a l l s and

l i n e r s ; i n s u f f i c i e n t l e n g t h of s t e e l l i n i n g ; b lockage

of a n a e r a t i o n d e v i c e a t a r a d i a l g a t e ; p r o v i s i o n of

a n i n s u f f i c i e n t a i r supp ly ; gap c a v i t a t i o n a t r a d i a l

and l e a f g a t e s , and f a i l u r e t o f o l l o w procedures

r egard ing symmetr ica l g a t e o p e r a t i o n .

C a v i t a t i o n damage i n t h e s l u i c e s of Libby and Dworshak

Dams (USA) i s d e s c r i b e d by Regan e t a 1 (1979). The

dams a r e of s i m i l a r d e s i g n , and each h a s t h r e e s l u i c e s

which a r e c o n t r o l l e d by r a d i a l t a i n t e r g a t e s and which

d i s c h a r g e on t o a c h u t e s p i l l w a y . A t Libby Dam, s t e e l

l i n e r s were used c l o s e t o t h e g a t e s but c a v i t a t i o n

damage occur red f u r t h e r downstream. A t Dworshak, one

s l u i c e was u n l i n e d , one was p r o t e c t e d by a 0.9mm t h i c k

epoxy p a i n t l a y e r , and t h e t h i r d by a 13mm t h i c k l a y e r

of epoxy g r o u t . A l l t h r e e s l u i c e s , i n c l u d i n g t h e

l i n i n g s , were damaged. The v e r t i c a l p r o f i l e s of t h e

s l u i c e s were des igned t o conform t o t h e t r a j e c t o r i e s

of f r e e j e t s . Inadequac ies i n t h e s e p r o f i l e s and i n

t h e i r c o n s t r u c t i o n were be l i eved t o have been t h e

cause of t h e c a v i t a t i o n .

J i n e t a 1 (1980) o b t a i n e d d a t a on t h e performance a£

158 g a t e s and s l o t s i n s t a l l e d i n 85 d i f f e r e n t p r o j e c t s

i n China. Of t h e Former t o t a l , 85 were o p e r a t i n g

g a t e s , 44 were emergency g a t e s and 29 were s e r v i c e

g a t e s f o r pens tocks ; 32 of t h e g a t e s have been s u b j e c t

t o some c a v i t a t i o n damage. The f o l l o w i n g c o n c l u s i o n s

were drawn From t h e s tudy :

1. more damage o c c u r s w i t h o p e r a t i n g g a t e s than

emergency ones due t o h i g h e r v e l o c i t i e s ,

lower p r e s s u r e s and more f r e q u e n t

o p e r a t i o n s ;

2. g a t e s l o t s near t h e upstream ends of t u n n e l s

a r e more l i a b l e t o damage because c u r v a t u r e

of t h e e n t r a n c e w a l l s produces low

p r e s s u r e s ;

3. damage i s more l i k e l y w i t h p a r t i a l l y - o p e n

g a t e s ;

4. damage is l i k e l y t o o c c u r a t p l a i n

r e c t a n g u l a r s l o t s i f t h e o p e r a t i n g head

exceeds 30m;

5. g a t e s l o t s wi th l e n g t h j d e p t h r a t i o s ( L / h ,

s e e F i g u r e 5) g r e a t e r t h a n 2.5 o r i n t h e

range 0.8-1.2 a r e l i a b l e t o cause damage.

Eros ion downstream of t h r e e c o n t r o l g a t e s l e d t o t h e

c o l l a p s e OF a 1 3 . 7 ~ d iamete r t u n n e l (No 2 ) a t T a r b e l a

Dam ( P a k i s t a n ) i n 1974. The main damage o c c u r r e d on

t h e i n v e r t of t h e t u n n e l o v e r a d i s t a n c e of about 45m

and reached a d e p t h of 5m. Kenn 6 Garrod (1981)

concluded t h a t t h i s e r o s i o n was t h e r e s u l t O F c a v i t i e s

o r i g i n a t i n g i n v e r t i c a l shear l a y e r s , which Formed a t

t h e downstream ends O F t h e w a l l s s e p a r a t i n g t h e t h r e e

g a t e s . The d i v i d e w a l l s themselves were a l s o damaged,

p o s s i b l y by c a v i t a t i o n i n h o r i z o n t a l s h e a r l a y e r s

caused by t h e g a t e s o p e r a t i n g under p a r t i a l l y

submerged c o n d i t i o n s . Eros ion s t a r t e d when t h e

v e l o c i t y i n t h e t u n n e l exceeded about 30mIs.

L e s l e i g h t e r (1983) d e s c r i b e s c a v i t a t i o n which o c c u r r e d

a t Dartmouth Dam ( A u s t r a l i a ) i n a 3m X 1.5m t u n n e l

downstream of c o n t r o l g a t e s o p e r a t i n g a t heads of up

t o 160m. The d e s i g n , which was based on t h e r e s u l t s

of a model t e s t , i n c l u d e d a s t a i n l e s s s t e e l l i n e r and

t h e u s e of compressed a i r i n j e c t e d i n t o t h e f low.

D e s p i t e t h e s e p r e c a u t i o n s , c a v i t a t i o n caused d e n t i n g

of t h e s t e e l l i n i n g . A f t e r f u r t h e r model t e s t i n g ,

ramps were added t o t h e s i d e w a l l s t o produce i n c r e a s e d

a e r a t i o n of t h e w a t e r .

Sharma h Goel (1983) g i v e d e t a i l s of damage i n a 7 . 6 2 1 ~

d i a m e t e r t u n n e l forming p a r t of t h e Beas S u t l e j L ink

P r o j e c t ( I n d i a ) . C a v i t a t i o n r e s u l t e d from f low

s e p a r a t i n g a t t h e downstream end of a c e n t r a l d i v i d i n g

w a l l . Negat ive p r e s s u r e s of 3-4m head of w a t e r were

measured, and e r o s i o n reached a d e p t h of 125-400mm.

The problem was remedied by s u p p l y i n g a i r t o a number

of n i p p l e s f i t t e d t o t h e s u r f a c e of t h e d i v i d e w a l l .

The c o n c r e t e was r e p a i r e d u s i n g 75mm t h i c k epoxy

m o r t a r w i t h two c o a t s of epoxy p a i n t .

Shengzhong (1984) r e p o r t s damage i n t h e s l o t s of two

g a t e s a t L i u j i a x i a Dam (China) . C a v i t a t i o n occur red

when t h e o p e r a t i n g head exceeded abou t 50m, and

o r i g i n a t e d a t t h e p o i n t where t h e g a t e r a i l formed a

n o t c h i n t h e downstream f a c e of each s l o t . The

problem was s t u d i e d i n a model, and s o l v e d by f i l l i n g

i n t h e n o t c h t o g i v e a rounded c o r n e r .

In Canada serious cavitation damage was reported by

Yung & Pataky (1986) to have occurred at the gate

slots of two spillways and also downstream of a

bulkhead gate in a low-level outlet. At Terzaghi Dam

(Canada) low-level gated outlets discharging through a

plug in the diversion tunnel caused cavitation erosion

downstream. As a result steel constrictors were

installed in the outlets downstream of the gates, and

these satisfactorily prevented further damage.

These examples suggest that cavitation in tunnels can

be due to a variety of factors, and that often the

cause is specific to the particular project. Remedial

measures also differ, and include use of alternative

lining materials, modifications to the flow geometry

and injection of air.

C.3 Design of gates Horizontal loads on vertical lift gates are

transferred to rails or bearing plates, which are

usually placed in vertical slots in the side walls so

as to remove them from regions of high-velocity flow.

Cavitation problems can be avoided completely by

locating the slots on the upstream side of the gate,

but this leads to structural difficulties and is not

common. Alternatively, with slots on the downstream

side, sliding plates can be fitted to the gate in

order to close off each slot and present a smooth

boundary to the flow. However, this solution requires

deep wells to accept the cover plates when the gate is

in its closed position. Therefore, in most cases, the

gate slots are located on the downstream side of

vertical gates and are open to the flow. Several

model studies have been carried out to establish

suitable shapes of slot for cavitation-free

operation.

B a l l (1959) d e s c r i b e s t h e r e s u l t s of e x t e n s i v e s t u d i e s

c a r r i e d o u t by t h e US Bureau of Reclamation. Designs

were t e s t e d i n w a t e r o r a i r t u n n e l s by measuring

p r e s s u r e s around t h e p e r i m e t e r s of t h e s l o t s ; some

t y p i c a l shapes a r e shown i n F igure 5. The lowes t

p r e s s u r e s occur red e i t h e r on t h e downstream f a c e of

t h e s l o t , o r on t h e channel w a l l a d j a c e n t t o i t .

Changes which r a i s e d t h e p r e s s u r e i n t h e s l o t tended

t o lower i t on t h e downstream w a l l , and v i c e v e r s a .

R e s t r i c t i n g the amount of c i r c u l a t i o n i n t h e s l o t by

keeping i t a s narrow a s p o s s i b l e was b e n e f i c i a l .

B a l l found t h a t a s imple r e c t a n g u l a r s l o t (Type 1A)

was s a t i s f a c t o r y f o r heads of up t o 10m; t h e p r e s s u r e

i n t h e s l o t ( r e l a t i v e t o t h e f ree - s t ream v a l u e ) was

p o s i t i v e , b u t n e g a t i v e on t h e downstream wal l . Adding

a d e f l e c t o r a t t h e upst ream edge lowered p r e s s u r e s i n

t h e s l o t , and would no t be a a t i s f a c t o r y u n l e s s t h e

d e f l e c t o r were l a r g e enough t o produce s t r o n g

a e r a t i o n . O f f s e t t i n g o r s l o p i n g t h e downstream w a l l

away from t h e f low (Types 1 B and 2A) d i d not improve

t h e o v e r a l l performance. Type 3C w i t h a converging

w a l l and rounded t r a n s i t i o n (n = 24, r Z 300mm) was

f a i r l y good, but t h e b e s t d e s i g n s s t u d i e d were Type 4b

( r a d i u s e d t r a n s i t i o n , 100 S r / t < 250) and Type 5A

( e l l i p t i c a l t r a n s i t i o n , E / t = 4 o r 5 ) . A s a l r e a d y

mentioned, t h e s l o t s were e v a l u a t e d by measur ing

p r e s s u r e changes. However, t h e r e c t a n g u l a r s l o t was

a l s o s t u d i e d i n a c a v i t a t i o n t u n n e l : c a v i t a t i o n was

found t o o c c u r a t a h i g h e r v a l u e of K t h a n p r e d i c t e d ,

probably because t h e s u r f a c e t a p p i n g s d i d n o t r ecord

t h e minimum p r e s s u r e i n t h e f low.

Rosanov e t a 1 (1965) used a c a v i t a t i o n t u n n e l t o t e s t

s e v e r a l t y p e s of g a t e s l o t . Values of t h e i n c e p t i o n

paramete r K were g i v e n s e p a r a t e l y f o r t h e upstream i

and downstream c o r n e r s of t h e s l o t . For a sharp-edged

ups t ream c o r n e r ( a s a l l those i n F i g 5 ) K = 1.15; i

rounding t h e edge reduced t h e v a l u e s l i g h t l y t o

Ki = 1.05. R e s u l t s f o r v a r i o u s t y p e s of downstream

c o r n e r a r e a s f o l l o w s :

Values a r e a l s o g i v e n i n t h i s r e f e r e n c e f o r s e v e r a l

more unusua l s l o t s w i t h d e f l e c t o r s , a i r p i p e s and

d e n t a t i o n s .

Three d e s i g n s of v e r t i c a l s l o t were t e s t e d by Adami

(1974) u n d e r c o n d i t i o n s of f r e e - s u r f a c e f low : Type 1 A

( w i t h L/h = 1.0-2.5); Type 4A ( w i t h L/h = 1.32, r /L =

0 .22) ; Type 1 B ( w i t h Llh = 1.0-2.5, t / h = 0.40) .

P r e s s u r e s i n t h e s l o t s were measured by means of

t a p p i n g s , and t e s t s were performed w i t h and w i t h o u t a

p a r t i a l l y - o p e n g a t e upst ream of t h e s l o t s . The

measurements i n d i c a t e d t h a t t h e p r e s s u r e s i n t h e s l o t s

were c l o s e t o h y d r o s t a t i c under a l l t h e c o n d i t i o n s

s t u d i e d ; t h e l a r g e s t n e g a t i v e d e p a r t u r e from

h y d r o s t a t i c p r e s s u r e was e q u i v a l e n t t o -0.059 t i m e s

t h e v e l o c i t y head of t h e f low. It was concluded t h a t

c a v i t a t i o n shou ld no t occur provided s u f f i c i e n t a i r

was s u p p l i e d t o m a i n t a i n a tmospher ic p r e s s u r e above

t h e f r e e s u r f a c e of t h e f low.

G a l p e r i n e t a 1 (1977) a n a l y s e d t h e r e s u l t s of s e v e r a l

s t u d i e s on c a v i t a t i o n a t sharp-edged g a t e s l o t s . The

e f f e c t s of v a r i o u s g e o m e t r i c f a c t o r s on t h e v a l u e of

K were p r e s e n t e d i n t h e form i

i n which Kis i s t h e v a l u e f o r i n c i p i e n t c a v i t a t i o n a t

t h e upst ream o r downstream edge of a square-shaped

s l o t ; Kis depends on ly upon t h e d e p t h h of the s l o t

r e l a t i v e t o t h e width B of t h e c o n d u i t . The f a c t o r s

c l , C* , c 3 t a k e account r e s p e c t i v e l y of t h e

length- to-depth r a t i o of t h e s l o t , t h e amount of any

o f f s e t i n t h e downstream w a l l , and t h e r e l a t i v e

t h i c k n e s s 6 of t h e boundary l a y e r ; 6 was c a l c u l a t e d

from t h e boundary l a y e r e q u a t i o n f o r smooth- turbulent

f low:

where X i s t h e l o n g i t u d i n a l d i s t a n c e from t h e s t a r t of

t h e boundary l a y e r . The e x p e r i m e n t a l r e s u l t s a r e

reproduced g r a p h i c a l l y i n F i g 6. These show t h a t t h e

s i z e of t h e c o n d u i t has a s i g n i f i c a n t e f f e c t on K i f i s

~ / h < 5, and t h a t r educ ing t h e s i z e of t h e c o n d u i t

i n c r e a s e s K is ' Use of a n o f f s e t i n c r e a s e s t h e

p r e s s u r e a t t h e downstream edge of t h e s l o t and

the reby reduces t h e tendency t h e r e f o r c a v i t a t i o n .

However, an o f f s e t a l s o r a i s e s t h e v a l u e of K f o r t h e i

upstream edge; t h i s i s because t h e o f f s e t weakens t h e

v o r t e x i n t h e s l o t and i n t e n s i f i e s t h e e d d i e s formed

by t h e f low s e p a r a t i n g a t t h e upst ream edge. C a v i t i e s

g e n e r a t e d a t t h e upst ream edge w i l l n o t cause damage

u n t i l the c a v i t a t i o n plume e x t e n d s f a r enough t o r e a c h

t h e downstream f a c e of t h e s l o t ; measurements i n d i c a t e

t h a t t h i s o c c u r s when t h e c a v i t a t i o n number K of t h e

f l o w i s l e s s than 0.6 K . . R e s u l t s such a s t h e s e app ly 1

when a g a t e i s f u l l y open and t h e f low p a s t t h e s l o t

i s approx imate ly two-dimensional.

G a l p e r i n e t a 1 a l s o g i v e d a t a f o r l e a f g a t e s t h a t a r e

p a r t i a l l y open. I f t h e s u p p o r t i n g mechanism of t h e

g a t e does no t f u l l y occupy t h e s l o t , downward f low

w i l l o c c u r w i t h i n t h e s l o t and w i l l i n c r e a s e t h e v a l u e

of Ki. C a v i t a t i o n damage t e n d s t o occur f i r s t on t h e

w a l l immediate ly downstream of t h e s l o t , a t t h e l e v e l s

of t h e g a t e l i p and t h e f l o o r . The l a t t e r damage i s

due t o t h e downward f l o w i n t h e s l o t which develops

i n t o a s p i r a l v o r t e x t h a t i s drawn o u t a t f l o o r l e v e l .

A t g a t e openings of l e s s t h a n 60% t h e damage on t h e

w a l l t e n d s t o be c o n c e n t r a t e d n e a r t h e f l o o r . F o r

g a t e s d i s c h a r g i n g under submerged c o n d i t i o n s , t y p i c a l

v a l u e s of K ( c a l c u l a t e d i t i s thought f o r a r e f e r e n c e i

p o i n t i n t h e j e t j u s t downstream of t h e g a t e ) can v a r y

between K = 1.0 a t a g a t e opening of 35% and K = 2.5 i i

a t an opening of 90%. For g a t e s d i s c h a r g i n g f r e e l y ,

t h e v a l u e s a r e lower and i n t h e range K = 0.3-1.0. i

For p a r t i a l l y - o p e n g a t e s , o f f s e t t i n g t h e w a l l

downstream of t h e g a t e s l o t i s on ly b e n e f i c i a l i n

r e d u c i n g K i f t h e r e i s f r e e - s u r f a c e f low downstream i

of t h e g a t e .

S e r i o u s c a v i t a t i o n can be caused by h i g h p r e s s u r e f l o w

th rough s m a l l gaps a t s e a l s and a t g a t e s t h a t a r e j u s t

opening o r c l o s i n g . C a v i t i e s may be g e n e r a t e d i n t h e

g a p i t s e l f due t o f low s e p a r a t i o n a t t h e upst ream end,

o r i n t h e t u r b u l e n t s h e a r l a y e r bounding t h e

h i g h - v e l o c i t y f low downstream of t h e gap. The v a l u e

of K depends upon t h e shape of t h e gap, and a c c o r d i n g i

t o Gaper in e t a 1 c a n v a r y from abou t 3.5-4.0 f o r a

sharp-edged e n t r a n c e t o 0.4-0.5 f o r a smoothly-shaped

one. Gate s e a l s should t h e r e f o r e have rounded

p r o f i l e s on t h e upst ream s i d e . T e s t s showed t h a t

s e a l s w i t h gaps of l e s s t h a n O . l m m a r e s a f e f o r s h o r t

p e r i o d s ; gaps of more than 2mm can cause s e r i o u s

e r o s i o n , and t h e s e a l s may themselves be damaged by

v i b r a t i o n s induced by u n s t a b l e c a v i t y f o r m a t i o n .

R a d i a l g a t e s have t h e advantage of no t r e q u i r i n g

s l o t s , but they can be d i f f i c u l t t o o p e r a t e under

pa r t i a l ly - submerged c o n d i t i o n s because t h e t r u n n i o n s

a r e s u b j e c t e d t o f l u c t u a t i n g flow f o r c e s . Under t h e s e

c o n d i t i o n s ( such a s occur i n n a v i g a t i o n l o c k s ) , a

r e v e r s e r a d i a l g a t e may be more s u i t a b l e . The s e a l s

of a r a d i a l g a t e can be a t t a c h e d t o t h e g a t e (which

a l l o w s t h e c o n d u i t w a l l s t o be kep t smooth), o r

o f f s e t s can be i n t r o d u c e d i n t h e s i d e s and f l o o r of

t h e condui t t o a c c e p t r e c e s s e d s e a l s ; t h e l a t t e r type

a r e e i t h e r i n f l a t a b l e o r t h e g a t e is p r e s s e d t i g h t

a g a i n s t them by means of s p e c i a l cams. G a l p e r i n e t a 1

d e s c r i b e r e s u l t s of c a v i t a t i o n t e s t s w i t h t h r e e types

of r a d i a l g a t e . For a normal r a d i a l g a t e w i t h

a t t a c h e d s e a l s , c a v i t a t i o n under submerged c o n d i t i o n s

o c c u r s a l o n g t h e bottom edge of t h e g a t e , and i s

p a r t i c u l a r l y i n t e n s e a t t h e s i d e w a l l s . Values of K i

v a r i e d between about K = 1.1 a t g a t e openings of up i

t o 60% and K = 1.4 a t an opening of 80%. C a v i t i e s i

a r e a l s o g e n e r a t e d downstream of t h e g a t e i n t h e s h e a r

l a y e r between t h e j e t and t h e s u r f a c e r o l l e r . Under

f ree - f low c o n d i t i o n s , c a v i t a t i o n i s g e n e r a t e d only a t

s u r f a c e i r r e g u l a r i t i e s . I n t h e c a s e of a r e v e r s e

r a d i a l g a t e , c a v i t a t i o n a g a i n o c c u r s a t t h e bottom

edge b u t i s more i n f l u e n c e d by t h e shape of t h e l i p ;

f o r a s h a r p k n i f e edge K 2 and f o r a s t r e a m l i n e d i

one K 1 . 3 For a normal r a d i a l g a t e w i t h r e c e s s e d i

s e a l s , c a v i t a t i o n d e v e l o p s a t t h e o f f s e t s i n t h e

condui t w a l l s i n a s i m i l a r way t o c a v i t a t i o n a t t h e

upst ream edge of a s l o t . Under submerged c o n d i t i o n s ,

K was found t o vary from about 1 .2 t o 1.8 a s t h e g a t e i

opening was i n c r e a s e d from 20% t o 60%. For f ree - f low

c o n d i t i o n s , t h e maximum v a l u e of K . was abou t 0.3 a t a 1

g a t e opening of 50%.

G a l p e r i n e t a 1 concluded t h a t , from t h e point-of-view

of c a v i t a t i o n , r a d i a l g a t e s have an advantage over

l e a f g a t e s on ly under f r ee - f low c o n d i t i o n s , and then

on ly i n t h o s e c a s e s where t h e c o n d u i t w a l l s cannot be

o f f s e t downstream of t h e s l o t s r e q u i r e d f o r t h e l e a f

g a t e s . A e r a t i o n of g a t e s e a t s was recommended a s a

means of p r e v e n t i n g damage due t o c a v i t a t i o n a t g a t e s

and a t s u r f a c e i r r e g u l a r i t i e s on t h e downstream w a l l s

of c o n d u i t s ( s e e S e c t i o n F.4).

Mean and f l u c t u a t i n g p r e s s u r e s were measured by

Ethembabaoglu (1978, 1979) i n s l o t s of Type l A , l B , 5A

and 5B. The l eng th - to -dep th r a t i o was v a r i e d f o r

v a l u e s of L/h S 5. The e l l i p t i c a l t r a n s i t i o n (Type 5A

w i t h t / h = 0.2 and E = h) gave t h e b e s t performance of

t h o s e t e s t e d , conf i rming t h e f i n d i n g s of B a l l and

Rosanov d e s c r i b e d p r e v i o u s l y . The l a r g e s t p r e s s u r e

f l u c t u a t i o n s o c c u r r e d a t t h e downstream edge of each

s l o t , and were maximum f o r l e n g t h r a t i o s of

3.0 S L/h 3.5; t h e maximum r o o t mean s q u a r e

p r e s s u r e f l u c t u a t i o n was 0.24 (pV 2 /2 ) , where V. i s 0

t h e u n d i s t u r b e d f low v e l o c i t y . The f requency of t h e

v o r t i c e s which formed i n t h e s l o t was p r e d i c t e d q u i t e

w e l l by t h e t h e o r e t i c a l formula

where N is t h e number of v o r t i c e s i n t h e s l o t . One

v o r t e x o c c u r r e d when L/h 1 . 2 , and two f o r ~ / h > 1.2

(up t o t h e v a l u e of L/h = 5 s t u d i e d i n t h e t e s t s ) .

J i n e t a 1 (1980) c a r r i e d o u t e x t e n s i v e tests i n a

c a v i t a t i o n t u n n e l t o de te rmine how t h e pa ramete r K i

v a r i e s w i t h t h e geometry of t h e g a t e s l o t . Two

s o u r c e s of c a v i t a t i o n can exist s i m u l t a n e o u s l y i n a

s l o t : " f i x e d " c a v i t a t i o n due t o f low s e p a r a t i o n , and

" v o r t e x " c a v i t a t i o n due t o t h e fo rmat ion of one o r

more v o r t i c e s i n t h e s l o t . I n narrow s l o t s ( e g , 0.75

S L/h S 1.5) v o r t e x c a v i t a t i o n predominates and

de te rmines the o v e r a l l K v a l u e of t h e s l o t . I n w i d e r i

s l o t s ( e g , 2.0 < ~ / h .S 3.5) t h e v o r t e x becomes weaker

and t h e K v a l u e is determined by t h e f i x e d i

c a v i t a t i o n .

The tests showed t h a t , f o r s a t i s f a c t o r y performance,

g a t e s l o t s shou ld have l e n g t h l d e p t h r a t i o s i n t h e

range 1.4 4 ~ / h S 2.5; b e s t r e s u l t s a r e o b t a i n e d i f

1.6 < L/h S 1.8. Measurements of K f o r p l a i n i r

r e c t a n g u l a r g a t e s l o t s of Type 1 A were d e s c r i b e d by

t h e e m p i r i c a l formula

Ki r = 0.38 (L/h) , f o r 1.5 .S L/H < 3.5 ( c . 4 )

The v a l u e s of t h e c a v i t a t i o n paramete r were c a l c u l a t e d

us ing t h e a v e r a g e v e l o c i t y and p r e s s u r e j u s t upst ream

of t h e s l o t .

S l o t s of Type 38 w i t h o f f s e t s and s l o p i n g downstream

w a l l s have lower v a l u e s of K t h a n p l a i n r e c t a n g u l a r i

s l o t s . Values can be c a l c u l a t e d from t h e e m p i r i c a l

r e l a t i o n

where t is t h e amount of t h e o f f s e t and K is t h e i r

v a l u e f o r t h e p l a i n s l o t g i v e n by Equat ion C.4. The

s l o t s which were t e s t e d had downstream w a l l s w i t h a

s l o p e of n = 12. It was recommended t h a t t h e amount

of o f f s e t shou ld be i n t h e range 0.05 S t /L < 0.08.

T e s t s w i t h s l o t s of Type 2B showed t h a t c a v i t a t i o n

w i l l d e v e l o p on t h e downstream s l o p i n g w a l l a t

When n becomes l a r g e , o t h e r f e a t u r e s of t h e s l o t

predominate and determine i t s o v e r a l l va lue of K . If i

the downstream wall is to be protected with steel, it

was recommended that the slope should be in the range

10 ,< n ,< 12.

Rounding the downstream edge of the slot (as in Type

4A) gave lower critical cavitation numbers than the

corresponding rectangular slot. The results were

described by the empirical equation

where r is the radius of the edge and K. is obtained l r

from Equation C.4. Based on Equations C.5 and C.7 it

was found that the combined effect of an offset and a

rounded edge (as for Type 3D) could be approximated

by

This result shows that an offset is normally more

effective in reducing the value of K. than rounding. 1

Overall, Jin et a1 concluded that a simple rectangular

slot will be suitable if the cavitation number of the

flow has a value of K > 1. However, if K < 0.4, then

particular care is needed in the design, model testing

and construction of the gate slot. Comparison of the

model and prototype performance of gate slots for two

hydro-electric schemes indicated that the models

overestimated the actual values of K. by between 7% 1

and 16%. For design, it was recommended that a safety

factor of 20% be adopted.

Sharma h Goel (1983) stress the importance of removing

the downstream channel wall from the cavitation

collapse zone. Gate slots of Type 3A (t/L = 0.1-0.2,

n 3 10) and Type 4B ( t / ~ = 0.1-0.2, r/L >/S) are

recommended. The authors also discuss suitable shapes

of gate lips. Lips should be designed so that either

the flow separates cleanly at the upstream end of the

lip, or remains attached until it reaches the

downstream edge. If the flow separates and then

re-attaches to the lip a short distance downstream,

the flow becomes unstable and may produce cavitation

and also damaging vibration.

Measurements of mean and fluctuating pressures in

rectangular gate slots of Type 1A were made by Yue

(1984). Five types of flow pattern were observed

according to the lengthldepth ratio of the slot, which

was varied between L/h = 0.25-8.0. Measurements of

the velocity profiles showed that the free-stream flow

expanded into the slot at an angle of about 10'

relative to the floor of the channel.

Naudascher h Locher (1974) studied the flow-induced

vibrations of small rectangular walls projecting from

a plane surface. The walls were similar in shape to

irregularity Type SA in Fig 1, with values of L/h = 1

and 3; the width of the tunnel was 6h. With the

square wall the flow separated cleanly, but for ~ / h =

3 there was unstable re-attachment which resulted in

the rms forces being increased by a factor of 2.5;

stable re-attachment occurred when L/h > 4.5.

Cavitation started at a value of about K = 4 for both i

shapes of wall (defined using the velocity and static

pressure upstream of the wall). The effect of

oscillating the walls in the direction transverse to

the flow was also investigated: this increased the

forces considerably in the case of the square wall,

but had little effect when there was unstable

re-attachment. The results of the study give an

euado XTTnj asomTe uaqn axe% ajT1 1eJTalaA

e U0 in220 xq%~m q2~qn speoT aqa 30 uoyae2ypuy

APPENDIX D

ENERGY DISSIPATORS

This section is concerned with the particular problems

of energy dissipators in which high levels of

turbulence can result in cavitation.

Bowers 6 Tsai (1969) describe results from model

studies of spillway stilling basins. Maximum pressure

fluctuations occur downstream of the toe of the

hydraulic jump, and can be up to 40% of the incoming

velocity head. If drainage pipes below the surface of

a spillway discharge into a stilling basin, there is a

danger that positive pressure peaks in the basin could

result in large uplift forces on the spillway slabs.

Negative fluctuations can lead to cavitation if the

pressures drop close to vapour pressure.

Narayanan (1980) analysed data on pressure

fluctuations in hydraulic jumps, and concluded that

the rms variation was about 0.05 times the upstream

velocity head. The probability or intermittency of

pressures reaching vapour pressure (and hence

producing cavitation) was calculated by assuming that

the variations followed a normal distribution.

Measurements of the pressure fluctuations beneath free

and forced hydraulic jumps were made by Akbari et a1

(1982). For free jumps on plain horizontal floors,

the maximum rms pressure variations decreased from

about 5.3% of the upstream velocity head at a Froude

number of F l = 6.2 to 3.0% at F 1 = 11.5. In the case

of forced jumps produced by a sill, the maximum rms

fluctuations varied from about 5% to 8%, increasing as

the sill was moved closer to the toe of the jump; for

a given configuration, the relative degree of

turbulence decreased as F was made larger. 1

Lopardo et a1 (1982, 1984, 1985) compared measurements

of pressure fluctuations in a prototype stilling basin

and a 1:50 scale Froudian model. The rms values of

the fluctuations and the probabilities of occurrence

of different amplitudes were well predicted by the

model. The incidence of cavitation damage in the

prototype also correlated satisfactorily with the

model measurements; the results suggested that

cavitation may occur if the instantaneous pressure

falls below vapour pressure for more than 0.1% of the

time (in the first two papers, Lopardo et a1 referred

to a limiting intermittency of 2%). In general the

pressure variations were not distributed symmetrically

about the mean value (cf Narayanan's assumption

above). Tests on a 1:60 model of a second stilling

basin showed that the positive pressure fluctuations

were larger than the negative ones as long as the flow

remained attached to the spillway channel. However,

in separation zones (eg downstream of baffle blocks,

sills etc) the situation was reversed, and the

negative fluctuations became bigger than the positive

ones. Evidence from the prototype suggests that

models may tend to overestimate somewhat the amount of

this asymmetry. The maximum rms values of the

pressure fluctuations on the floor of the basin varied

between about 5% and 9% of the velocity head entering

the jump, depending upon the layout of the basin and

upon the entrance conditions. A pressure tapping in

the downstream face of a chute block indicated an rms

variation equal to 27% of the incoming velocity head.

Baffle blocks and other appurtenances used in stilling

basins need to have large drag coefficients to be

effective. However, the turbulence generated by the

blocks also tends to make them liable to cavitation

damage. Careful design is therefore needed to

reconcile the conflicting demands of good drag and

cavitation characteristics.

Research on the cavitation performance of baffle

blocks appears to have been mainly concentrated in the

USSR. Quintela h Ramos (1980) give a useful summary

of some of the Russian work which is not otherwise

readily available-

Iuditski (1965) studied cavitation at baffle blocks at

Novosibirsk Dam (USSR) using a 1:53 scale model in a

vacuum test rig. Points at which cavitation pressures

were recorded in the model coincided with those at

which damage had occurred in the prototype. Flow

separation at the upstream face of the blocks caused

erosion along the sides, while separation at the

downstream corners produced damage on the adjacent

areas of floor.

Pressure measurements at baffle blocks tend to

underestimate the value of the incipient cavitation

parameter because the lowest pressures do not occur at

the surface of the block. Rosanov et a1 (1965) found

that the true K is related to the value K. obtained i IP

from pressure measurements (allowing for fluctuations)

by

where F, = 1.8 for cubic shapes and 5 = 1.45 for

pyramidal and rhombic shapes.

Rozanov et a1 (1971) give values of the inception

parameter K. for various types of block. For a cube 1

of side lOOmm set normal to the flow K = 2.2, while i

rotating it through 45' reduces the figure to K = 1.1 i

(calculated using the depth of water above the block

and the velocity of flow entering the jump). Rounding

the corners lowers the value of K., but also reduces 1

the drag coefficient. Damage can also be controlled

by injecting air or water into the separation zones.

Comparative t e s t s were c a r r i e d o u t i n a c a v i t a t i o n

t u n n e l (no f r e e s u r f a c e ) and a vacuum t e s t r i g which

a l lowed t h e h y d r a u l i c jump t o be reproduced: t h e

c a v i t a t i o n t u n n e l gave v a l u e s of K lower by abou t i

10-20%. Labora to ry and f i e l d measurements i n d i c a t e d

t h a t t h e g r e a t e s t r a t e of damage t o t h e b l o c k s

occur red a t a c a v i t a t i o n i n t e n s i t y of abou t I = 0.7

( s e e Equa t ion 5 ) .

G a l p e r i n e t a 1 (1977) d e s c r i b e p r e s s u r e measurements

made on f o u r t y p e s of t r u n c a t e d pyramidal b a f f l e

b lock ; t h e s l o p e s of t h e ups t ream and downstream

f a c e s were r e s p e c t i v e l y 1:l and 1:0.5 ( v e r t i c a l :

h o r i z o n t a l . The s i d e s of t h r e e of t h e b l o c k s were

s l o p e d outwards i n t h e d i r e c t i o n of f low s o a s t o

f a c i l i t a t e t h e passage of i c e and f l o a t i n g d e b r i s .

T h i s s l o p i n g gave rise t o lower ( i e more a d v e r s e )

p r e s s u r e s t h a n a f o u r t h b a f f l e w i t h p a r a l l e l s i d e s .

Rounding t h e ups t ream c o r n e r s of pyramidal b l o c k s was

recommended t o reduce t h e danger of c a v i t a t i o n ( r a d i u s

= 0.05 times o v e r a l l b lock width) . The t r a n s v e r s e

d i s t a n c e between a d j a c e n t b a f f l e s was found no t t o

a f f e c t t h e v a l u e of K u n l e s s t h e c l e a r d i s t a n c e was i

l e s s t h a n 1.5 t i m e s t h e b lock width; r educ ing t h e

s p a c i n g reduced K G a l p e r i n e t a 1 a l s o g i v e r e s u l t s i '

f o r s i x t y p e s of wedge b l o c k which may be i n s t a l l e d i n

s i l l s a t t h e downstream ends of s t i l l i n g b a s i n s t o

i n c r e a s e t h e amount of ene rgy d i s s i p a t i o n ; t h e v a l u e s

of K i v a r i e d from 1.91 t o 1.05. J e t s p l i t t e r s may be

u s e d a t t h e downstream end of a s p i l l w a y t o form a

s l o t t e d l i p which b r e a k s up t h e f low i n t o upper and

lower j e t s . T e s t s showed t h a t s e r i o u s v o r t e x

c a v i t a t i o n w i l l beg in a l o n g t h e s i d e s of such

s p l i t t e r s a t abou t K = 0.7; rounding t h e l o n g i t u d i n a l i

e d g e s of t h e s p l i t t e r s ( r a d i u s = 0.07 t imes wid th of

s p l i t t e r ) reduced K t o abou t 0.15. i

I n g e n e r a l t h e most f a v o u r a b l e c a v i t a t i o n

c h a r a c t e r i s t i c s f o r b a f f l e b l o c k s a r e o b t a i n e d by

p l a c i n g a downstream s t e p i n t h e f l o o r , and s l o p i n g

t h e t o p and s i d e s of t h e b lock away from t h e f low s o

t h a t c a v i t i e s a r e p reven ted from c o l l a p s i n g a g a i n s t

any s o l i d s u r f a c e s . The concept can be ex tended t o

t h e d e s i g n of s u p e r c a v i t a t i n g b l o c k s i n which t h e f low

s e p a r a t e s t o form a f i x e d c a v i t y which e x t e n d s

downstream of t h e b lock . Oskolkov h Semenkov (1979)

g i v e d e t a i l s of f o u r t y p e s of s u p e r c a v i t a t i n g b l o c k ,

and t h e s e a r e reproduced i n F i g u r e 7 (Types 1-4).

Rozanova C A r i e l (1983) measured t h e d r a g c o e f f i c i e n t s

of f o u r k i n d s of b a f f l e b lock (Types 5-8 i n F i g u r e 7 ) ;

n o t e t h a t a l t h o u g h Types 2 and 8 a r e s i m i l a r i n shape ,

t h e y have d i f f e r e n t p r o p o r t i o n s . The t e s t s showed

t h a t t h e d r a g c o e f f i c i e n t of a b l o c k was c o n s t a n t f o r

v a l u e s of K > Ki, b u t d e c r e a s e d when c a v i t a t i o n

o c c u r r e d . The r e s u l t s were found t o f i t t h e formula

where C and C a r e r e s p e c t i v e l y t h e d r a g d do

c o e f f i c i e n t s w i t h and w i t h o u t c a v i t a t i o n . Values of

Cdo and K f o r t h e f o u r shapes t e s t e d a r e g iven i n

i F i g u r e 7.

J i n (1983) t e s t e d f o u r d e s i g n s of b a f f l e b l o c k , of

which one was of s u p e r c a v i t a t i n g t y p e . The

exper iments were c a r r i e d o u t u s i n g f r e e - s u r f a c e f l o w s

w i t h Froude numbers between 4.8 and 7.8. Measurements

were made of t h e c a v i t a t i o n i n d e x K and a l s o of t h e i

mean and f l u c t u a t i n g p r e s s u r e s on t h e s u r f a c e of t h e

b l o c k s . The p r e s s u r e f l u c t u a t i o n s v a r i e d between 0 . 5 1

and 0 .23 t imes t h e upst ream v e l o c i t y head, depending

upon t h e shape of t h e b lock and t h e Froude number of

t h e f low.

Energy can be dissipated in high-head tunnels by means

of sudden expansions which convert kinetic energy into

turbulence. Cavities are liable to be formed around

the perimeter of the high velocity jet, and can damage

the walls of the chamber if they are too close.

Tests on cylindrical expansions were carried out in a

cavitation tank by Rouse 6 Jezdinsky (1965, 1966).

The condition of incipient cavitation was determined

acoustically for different ratios of the upstream and

downstream pipe diameters, D and D Values of the U d'

incipient cavitation index (calculated using the

velocity and static pressure upstream of the

expansion) ranged from K = 0.6 at DU/Dd -0 to K. = i 1

0.45 at DU/Dd = 0.6. However, the more important

criterion is the parameter K at which damage starts id

to occur on the chamber walls: values were in the

range of Kid = 0.08 to 0.15, so that the use of K i

for design should provide a considerable safety

factor. Large positive pressure fluctuations take

place just upstream of the point at which the

high-velocity jet reattaches to the chamber wall, and

these can give rise to damaging structural

vibrations.

Russell 6 Ball (1967) used a 1:56.6 model to study the

design of a dissipator for Mica Dam in which three

conduits discharged into a single expansion chamber.

The cavitation parameter was defined as

in which P is the upstream total pressure and p is U d

the downstream static pressure. Values of K. proved 1

to be larger than expected, and were sensitive to

changes in the spatial configuration of the three

conduits. The model was tested under heads close to

those in the prototype (about 140m). Incipient

c a v i t a t i o n o c c u r r e d i n t h e range of K. = 2.5 t o 3.0 1

and damage s t a r t e d a t Kid = 0.6.

Ripken & Hayakawa (1972) s t u d i e d t h e performance of a

j e t - v a l v e d i s s i p a t o r u s i n g a model w i t h a n 83mm

d i a m e t e r o r i f i c e d i s c h a r g i n g i n t o a 152mm d i a m e t e r

c h a m b e r The c a v i t a t i o n parameter was d e f i n e d a s

C a v i t a t i o n s t a r t e d between K . = 1.7 and 2 .3 , and 1

damage a t t h e w a l l o c c u r r e d a t K = 0.58. The amount i d

of damage was reduced by add ing v o r t e x g e n e r a t o r s

around t h e p e r i m e t e r of t h e o r i f i c e . T h i s p e r m i t t e d a

r e d u c t i o n i n t h e l e n g t h of t h e expans ion chamber, b u t

i n c r e a s e d t h e v a l u e of K . . The d i f f e r e n t d e f i n i t i o n s 1

of K used i n t h e s e v a r i o u s s t u d i e s make i t d i f f i c u l t

t o compare r e s u l t s w i t h o u t hav ing a c c e s s t o t h e

o r i g i n a l d a t a .

S c a l e e f f e c t s i n model l ing c a v i t a t i o n i n sudden

en la rgements were i n v e s t i g a t e d by B a l l e t a 1 (1975).

The l i m i t of i n c i p i e n t c a v i t a t i o n was found t o v a r y

w i t h changes i n s i z e b u t n o t w i t h changes i n t h e

p r e s s u r e a t which t h e t e s t s were c a r r i e d o u t .

However, e x a c t l y t h e o p p o s i t e a p p l i e s t o t h e l i m i t of

i n c i p i e n t damage, which was d e f i n e d t o be a r a t e of 1

p i t f i n 2/minute on s o f t aluminium. Th i s d e f i n i t i o n i s

a conven ien t measure f o r e x p e r i m e n t a l work, b u t may

i t s e l f be s u b j e c t t o a type of s c a l e e f f e c t because

t h e volumes of t h e p i t s i n c r e a s e a s t h e s i z e of t h e

model i n c r e a s e s .

I n f o r m a t i o n on t h e r e l a t e d t o p i c of c a v i t a t i o n a t p i p e

o r i f i c e s i s provided by T u l l i s & Govindara jan (1973) .

The r a t i o of o r i f i c e d i a m e t e r t o p i p e d i a m e t e r , D o / D ,

was v a r i e d between 0 .33 and 0 .88 i n p i p e s w i t h

d i a m e t e r s r ang ing from 27.4mm t o 587mm. C a v i t a t i o n

was d e t e c t e d by changes i n t h e i n t e n s i t y of t u r b u l e n c e

recorded by a n a c c e l e r o m e t e r . Values of t h e i n c i p i e n t

c a v i t a t i o n parameter (de f ined a c c o r d i n g t o Equa t ion

D.4) v a r i e d f rom abou t K . = 1 .5 a t D /D = 0.4 t o l 0

Ki = 11 a t D / D = 0.8 . S c a l e e f f e c t s were found due 0

t o changes i n s i z e , b u t no t due t o changes i n p r e s s u r e

o r v e l o c i t y .

APPENDIX E

CAVITATION RESISTANCE OF MATERIALS

E . 1 Concre te Inozemtsev et a 1 (1965) c a r r i e d ouc a comprehensive

i n v e s t i g a t i o n of t h e f a c t o r s a f f e c t i n g t h e r e s i s t a n c e

of d i f f e r e n t c o n c r e t e s . Samples were t e s t e d i n a

l a b o r a t o r y w a t e r t u n n e l by p l a c i n g them downstream of

a c y l i n d e r which g e n e r a t e d c a v i t i e s i n i t s wake; t h e

f l o w v e l o c i t y i n t h e p l a n e of t h e c y l i n d e r was

26.4mls. The r a t e of l o s s of weight was recorded , and

a t e s t was t e r m i n a t e d i f t h e dep th of e r o s i o n reached

5mm.

Good r e s i s t a n c e c h a r a c t e r i s t i c s of c o n c r e t e were found

t o be a s s o c i a t e d wi th a h i g h compressive s t r e n g t h and

a low water lcement r a t i o . The c a v i t a t i o n r e s i s t a n c e

i s determined by t h e i n t e r n a l cohes ion of t h e b i n d e r

and by t h e adhes ion between t h e b i n d e r and t h e

a g g r e g a t e ; t h e s t r e n g t h of t h e a g g r e g a t e i t s e l f i s

n o t u s u a l l y a f a c t o r . Large, dense a g g r e g a t e s produce

low r e s i s t a n c e because t h e f o r c e s of a d h e s i o n a r e

weak; b e s t r e s u l t s a r e o b t a i n e d i f t h e a g g r e g a t e i s

porous , i f t h e cement and a g g r e g a t e a r e a s s i m i l a r i n

s i z e a s p o s s i b l e , and i f t h e a g g r e g a t e r e a c t s

chemica l ly wi th t h e cement.

Of t h e o r d i n a r y c o n c r e t e s t e s t e d , t h e h i g h e s t

r e s i s t a n c e occur red wi th cement c l i n k e r a g g r e g a t e

( l o s s r a t e o f 3 . l g I h o u r ) and t h e lowest wi th g r a v e l

a g g r e g a t e (32gIhour) ; crushed l i m e s t o n e and crushed

g r a n i t e were i n t e r m e d i a t e . Grinding of t h e cement

a l s o improved t h e e r o s i o n p r o p e r t i e s . and t h e optimum

f i n e n e s s was found t o be 4 0 0 0 c m ~ / ~ . Fine-g ra ined

vibromix c o n c r e t e and c o n c r e t e w i t h crushed g r a n i t e

and a u t o c l a v e c u r i n g were a b o u t 25 t imes more

r e s i s t a n t than g r a v e l c o n c r e t e .

P l a s t i c c o n c r e t e s were a l s o t e s t e d and were found t o

have r e s i s t a n c e s t h a t were 10-100 t imes h i g h e r t h a n

normal cement c o n c r e t e s . The l o s s r a t e s f o r

epoxy-po lyes te r p l a s t i c c o n c r e t e s w i t h sand and

g r a p h i t e a g g r e g a t e s were between 0.03 and 0 .2 lg lhour .

The b e s t r e s u l t s were o b t a i n e d w i t h a n epoxy- thiokol

p l a s t i c c o n c r e t e which had a performance s i m i l a r t o

t h a t of s t e e l , and showed no weight l o s s a f t e r 12

hours . A c o a t i n g of epoxy r e s i n improved t h e

c a v i t a t i o n r e s i s t a n c e of o r d i n a r y c o n c r e t e , and was

more e f f e c t i v e than u s i n g FA monomer.

The e f f e c t of s u r f a c e f i n i s h on t h e r a t e of c a v i t a t i o n

damage was i n v e s t i g a t e d by Thiruvengadam (1960).

S i m i l a r samples of g r a n i t e were p o l i s h e d and t h e n

roughened t o d i f f e r e n t d e g r e e s . It was found t h a t t h e

smoother t h e s u r f a c e , t h e lower was t h e i n i t i a l r a t e

of weight l o s s due t o c a v i t a t i o n . However, p o l i s h i n g

g i v e s on ly a temporary b e n e f i t s i n c e c a v i t a t i o n a t t a c k

w i l l e v e n t u a l l y roughen t h e s u r f a c e anyway.

Kenn (1971) t e s t e d samples of c o n c r e t e i n a c a v i t a t i o n

r i g s i m i l a r i n type t o t h a t used by Inozemtsev e t a 1

( s e e above) . Compressive s t r e n g t h s of 41.5MPa and

20.7MPa were o b t a i n e d w i t h water lcement r a t i o s of 0.60

and 0.80 r e s p e c t i v e l y ; t h e a g g r e g a t e s i z e was 10mm.

The c a v i t a t i o n r e s i s t a n c e of t h e normal 41.5MPa

c o n c r e t e was s i g n i f i c a n t l y h i g h e r t h a n t h a t of t h e

h a l f - s t r e n g t h m a t e r i a l . I t was a l s o found t h a t t h e

amount of damage could be much reduced by p r o t e c t i n g

t h e c o n c r e t e w i t h a 6mm t h i c k l a y e r of Renfor cement

o r Renfor t r o p i c a l g r o u t .

G a l p e r i n e t a 1 (1971) g i v e d a t a on t h e r e l a t i o n s h i p

between t h e f low v e l o c i t y i n a s t r u c t u r e and t h e

compress ive s t r e n g t h of c o n c r e t e needed t o resist

c a v i t a t i o n . The r e s u l t s were shown g r a p h i c a l l y but

can be approximated by

where V is t h e a l l o w a b l e v e l o c i t y i n m / s and M is the

compress ive s t r e n g t h i n MPa. For compressive

s t r e n g t h s i n t h e range 20 M < 50 MPa, t h e c o n s t a n t U

has a v a l u e of approx imate ly U = 1.5mIs.

Kudriashov e t a 1 (1983) a l s o p r e s e n t e d d a t a on

a l l o w a b l e f low v e l o c i t i e s a d j a c e n t t o c o n c r e t e

s u r f a c e s . The r e s u l t s agreed wi th t h e form of

Equa t ion ( E . l ) , b u t t h e v a l u e of t h e c o n s t a n t was

approx imate ly U = 3.0m/s f o r compress ive s t r e n g t h s o f

20 M S 50 MPa. According t o Novikova h Semenkov

(1985). t h e a l l o w a b l e v e l o c i t i e s g i v e n by Kudriashov

e t a 1 a r e f o r a n i n c u b a t i o n p e r i o d of 48 hours .

Allowable v e l o c i t i e s V f o r o t h e r p e r i o d s T ( i n h o u r s ) T

can be c a l c u l a t e d from

The u s e of s t e e l - f i b r e c o n c r e t e t o r e p a i r c a v i t a t i o n

damage a t Libby Dam (USA) i s d e s c r i b e d by Schrader h

Munch (1976). The o r i g i n a l c o n c r e t e which was eroded

was of good q u a l i t y w i t h a water lcement r a t i o of

0.34-0.42 and a compress ive s t r e n g t h a t 90 days o f

43.1MPa. T h i s was r e p l a c e d wi th c o n c r e t e c o n t a i n i n g

1% of 25mm long s t e e l f i b r e s (0.36-0.40 wate r lcement

r a t i o , 19mm maximum a g g r e g a t e s i z e , 433kg/m3 of cement

and abou t 5% e n t r a i n e d a i r ) . The compress ive s t r e n g t h

a t 28 days was 48.0-55.OMPa, and a t 90 days exceeded

67.1MPa. The m a t e r i a l was s t i f f u n l e s s v i b r a t e d , b u t

was p laced s u c c e s s f u l l y and had a n appearance and

s u r f a c e t e x t u r e s i m i l a r t o t h a t of t h e o r i g i n a l

c o n c r e t e . F i b r o u s c o n c r e t e was a l s o used f o r r e p a i r s

a t Dworshak Dam (USA), and Regan et a 1 (1979) r e p o r t

t h a t no s i g n i f i c a n t e r o s i o n of t h e new m a t e r i a l

o c c u r r e d .

At Dworshak Dam some of the fibrous concrete was also

polymerized to increase further its durability.

Details of the technique are given by Murray h

Schultheis (1977) and by Stebbins (1978), and

consisted essentially of soaking an area of cured

concrete with a monomer which was then polymerized by

the application of heat. The constituents by weight

of the monomer were 95% methylmethacrylate (MMA), 5%

trimethylolpropane trimethacrylate (TMPTMA,

cross-linking agent) and 0.5% catalyst. Before

applying the monomer it was necessary to dry the

concrete, and this was done by using infra-red lamps

to heat it to a temperature between 127'C and 150°C

for 8 to 10 hours. The concrete was then allowed to

cool to 3B0C, after which it was soaked with monomer

for 5 to 6 hours. Polymerization was achieved by

heating for 2 hours to a temperature between 65'C and

99'C using water or dry steam. The technique was

carried out on both horizontal and vertical areas of

concrete and was considered viable, although it did

require careful control. The fibrous concrete was

polymerized to a depth of up to 38mm, and this

increased its compressive strength from 55MPa to about

140MPa.

Galperin et a1 (1977) explain how a denser finish to

the concrete surface of the spillway at Krasnoyarsk

Dam (USSR) was obtained using absorptive and vacuum

formwork. The absorptive panels were lined with

timber-fibre sheets covered with dense coarse calico,

and were used successfully for the straight sections

of the spillway. The vacuum forms were used for the

curved sections of the spillway bucket, but movements

of the panels gave rise to steps of up to 30-40mm in

height. Galperin et a1 also give test results which

showed that adding a relatively small amount of a

polymer to concrete could increase its cavitation

resistance by a factor of up to 50. Gunite

( s h o t c r e t e ) was a l s o found t o have good c a v i t a t i o n -

r e s i s t i n g p r o p e r t i e s .

Lowe e t a 1 (1979) d e s c r i b e comparat ive c a v i t a t i o n

t e s t s on d i f f e r e n t c o n c r e t e s which were c a r r i e d o u t i n

c o n n e c t i o n w i t h t h e r e p a i r s t o T a r b e l a Dam ( P a k i s t a n ) .

Regu la r c o n c r e t e ( w i t h a 28 day compress ive s t r e n g t h

of 31.0MPa) e roded t o a depth of 75mm t h r e e times a s

q u i c k l y a s d i d s t e e l - f i b r e c o n c r e t e (41.4MPa a t 28

d a y s ) and polymerized o r d i n a r y c o n c r e t e . I n t h e c a s e

of polymerized f i b r o u s c o n c r e t e t h e d e p t h of e r o s i o n

d i d n o t exceed 25mm. With t h e f i b r o u s c o n c r e t e i t was

p o s s i b l e t o use a h i g h e r cement r a t i o because t h e

s t e e l f i b r e s p reven ted t h e c r a z i n g which would

o t h e r w i s e have occur red .

D e t a i l s of t h e remedia l works c a r r i e d ou t a t T a r b e l a

D a m a r e g i v e n by Chao (1980) . Damaged a r e a s were

i n i t i a l l y r e p a i r e d u s i n g r e g u l a r c o n c r e t e ( w i t h a

compress ive s t r e n g t h of 41.4MPa) and two c o a t s of

epoxy s e a l . Some of t h i s c o n c r e t e subsequen t ly f a i l e d

due t o c r a c k i n g and was rep laced w i t h 27.6MPa

c o n c r e t e . The epoxy s e a l a l s o f a i l e d due t o p o o r

a d h e s i o n . A t o t a l of 6000m3 of f i b r o u s c o n c r e t e was

used t o r e i n s t a t e some of t h e f l o o r s l a b s of t h e

s t i l l i n g b a s i n s , and i n c o n j u n c t i o n w i t h a n a e r a t i o n

s l o t performed s a t i s f a c t o r i l y a t f low v e l o c i t i e s up t o

47mls.

J i a n g h Chen (1982) t e s t e d samples of c o n c r e t e i n a

c a v i t a t i o n t u n n e l t o i n v e s t i g a t e how t h e c a v i t a t i o n

r e s i s t a n c e was a f f e c t e d by f a c t o r s such a s t h e

water /cement r a t i o , t h e use of a d d i t i v e s and t h e a g e

of t h e c o n c r e t e . It was found t h a t t h e c a v i t a t i o n

r e s i s t a n c e R ( d e f i n e d a s t h e i n v e r s e of t h e r a t e of C

l o s s of weight p e r u n i t a r e a ) v a r i e d w i t h t h e

water lcement r a t i o (W/C) a s

and wi th t h e compressive s t r e n g t h M a s

Preece h Hansson (1983) c a r r i e d o u t t e s t s which showed

t h a t t h e c a v i t a t i o n r e s i s t a n c e of o r d i n a r y c o n c r e t e

could be improved by u s i n g a s u l p h a t e - r e s i s t a n t

p o r t l a n d cement c o n t a i n i n g s i l i c a p a r t i c l e s (known

commercially a s "Dens i t " ) . These p a r t i c l e s have a

s i z e of abou t 0 . 1 ~ (compared w i t h t h e 1 0 O p of normal

cement p a r t i c l e s ) , and t h e r e f o r e produce a dense

m o r t a r which i s a b l e t o f i l l t h e i n t e r s t i c e s of t h e

a g g r e g a t e and t h u s g i v e a s t r o n g bond.

Schrader (1983) surveyed t h e p r a c t i c a l a s p e c t s of

c o n s t r u c t i n g c o n c r e t e s t r u c t u r e s t o avo id o r r e s i s t

c a v i t a t i o n . Unwanted o f f s e t s a t j o i n t s a r e sometimes

caused by t h e d i f f i c u l t y of a l lowing f u l l y f o r

s h r i n k a g e , d i f f e r e n c e s i n h e a t of h y d r a t i o n , e t c .

T i g h t t o l e r a n c e s do n o t n e c e s s a r i l y p reven t t h e

occur rence of s i g n i f i c a n t s l o p e changes . A s a n

example, a l i m i t of 1.5mm d e v i a t i o n p e r 300mm could

r e s u l t i n a s l o p e change of 1 /25 , whi le a seemingly

l e s s s e v e r e c r i t e r i o n of 6mm p e r 3000mm would r e s t r i c t

t h e change t o 1/60. Designers need t o t a k e account of

t h e p r a c t i c a l problems of p l a c i n g c o n c r e t e when

d e s i g n i n g re in forcement . I f placement i s d i f f i c u l t , a

c o n t r a c t o r w i l l t end t o u s e a f i n e r a g g r e g a t e and a

h i g h e r w a t e r c o n t e n t , which reduces t h e s t r e n g t h of

t h e c o n c r e t e and i n c r e a s e s t h e amount of h e a t i n g and

shr inkage .

At tempt ing t o o b t a i n a smooth f i n i s h by overworking

t h e newly-placed c o n c r e t e wi th a t r o w e l produces a

s o f t e r s u r f a c e t h a t i s l i a b l e t o c r a z e . Grinding t o

remove i r r e g u l a r i t i e s can be d e t r i m e n t a l because i t

t a k e s away p a r t s of t h e a g g r e g a t e which may then be

plucked o u t more e a s i l y by t h e f low; t h e sudden

change i n s u r f a c e roughness may a l s o promote

c a v i t a t i o n downstream.

Great c a r e i s needed when pa tch ing . Where p o s s i b l e

t h e new m a t e r i a l should be of t h e same mix a s t h e

su r rounding c o n c r e t e ; i d e a l l y t h e two m a t e r i a l s

shou ld have t h e same m o r t a r and a g g r e g a t e , s i m i l a r

s u r f a c e t e x t u r e and e q u a l c o e f f i c i e n t s of s h r i n k a g e

and thermal expansion. I f t h e p a t c h i s h a r d e r t h a n

t h e su r rounding c o n c r e t e , i t w i l l t e n d t o p r o j e c t

above i t . Pa tches can a l s o s h r i n k away from t h e base

m a t e r i a l , and t h u s be plucked ou t complete ly by t h e

f low.

Although epoxy m a t e r i a l s have a good c a v i t a t i o n

r e s i s t a n c e , they may f a i l due t o t h e f o r m a t i o n of a

"g lue- l ine" a t t h e edges of t h e su r rounding c o n c r e t e .

Water o r vapour p r e s s u r e , o r t h e e f f e c t s of

d i f f e r e n t i a l expansion o r sh r inkage can cause t h e

c o n c r e t e below t h e g l u e - l i n e t o f a i l s o t h a t t h e epoxy

is l o s t i n a lump; i t is t h e r e f o r e impor tan t t o

o b t a i n good c o n t i n u i t y a t t h e j o i n t . The d i f f e r e n c e

i n s u r f a c e t e x t u r e between epoxy m a t e r i a l s and

c o n c r e t e can be c o n s i d e r a b l e , and may g i v e r i s e t o

c a v i t a t i o n .

Polymeriz ing c o n c r e t e i n c r e a s e s i t s s t r e n g t h and

c a v i t a t i o n r e s i s t a n c e by a f a c t o r of t h r e e , and i s

e f f e c t i v e i n producing a good bond a t j o i n t s and

r e p a i r s . However, i t is a l s o expens ive . S t e e l - f i b r e

c o n c r e t e has proved s u c c e s s f u l , but may s t i l l be

e roded by t h e g r i n d i n g a c t i o n oE d e b r i s ( eg i n

s t i l l i n g b a s i n s ) . Adding 0.5-1.5% by volume of s t e e l

f i b r e s i n c r e a s e s t h e c a v i t a t i o n r e s i s t a n c e by a f a c t o r

of t h r e e , but has l i t t l e e f f e c t on s t r e n g t h . The

E.2 Metals

f i b r e s a r e e f f e c t i v e because they e n a b l e t h e c o n c r e t e

t o a b s o r b high-frequency impacts wi thou t s u f f e r i n g

f a t i g u e f a i l u r e .

Zheng (1984) measured t h e c a v i t a t i o n r e s i s t a n c e of

bitumen m o r t a r , and showed t h a t , under c e r t a i n

c o n d i t i o n s , i t was s l i g h t l y h i g h e r than t h a t of

o r d i n a r y cement mor ta r . Unl ike most o t h e r m a t e r i a l s ,

t h e r e s i s t a n c e of t h e bitumen m o r t a r was found t o

i n c r e a s e a s i t s e l a s t i c modulus decreased .

The American Concre te I n s t i t u t e i s p r e p a r i n g a g u i d e

on t h e e r o s i o n of c o n c r e t e which i n c l u d e s s e c t i o n s on

c a v i t a t i o n damage and methods of r e p a i r , but a t t h e

t ime of w r i t i n g t h i s had n o t been pub l i shed .

A c o n s i d e r a b l e amount of l a b o r a t o r y work has been

c a r r i e d o u t t o compare t h e r e s i s t a n c e of d i f f e r e n t

m e t a l s t o c a v i t a t i o n . Nousson (1937) t e s t e d a l a r g e

number of steels and o t h e r m e t a l s i n a v e n t u r i t u n n e l

u s i n g w a t e r a t 2 0 ° C , and measured t h e l o s s of volume

which o c c u r r e d a f t e r 16 hours . The r e s u l t s show t h a t

t h e amount of damage v a r i e s w i ~ h t h e chemical c o n t e n t

of t h e meta l and a l s o w i t h t h e method of forming ( e g

c a s t , r o l l e d o r f o r g e d ) . A s m a l l s e l e c t i o n of t h e

d a t a is g i v e n below t o i l l u s t r a t e t h e range of v a l u e s

ob ta ined . The v a l u e s of volume l o s s a r e on ly r e l a t i v e

s i n c e they a r e s p e c i f i c t o t h e type of equipment and

i n t e n s i t y of c a v i t a t i o n used i n t h e t e s t s .

M e t a l

aluminium a l l o y

phosphor copper bronze

c a s t i r o n

Mn bronze

Volume l o s s a f t e r 16 hours

(mm 3,

Low-alloyed steels

0.30% r o l l e d carbon s t e e l

0.33% c a s t carbon steel

0.22% forged carbon s t ee l

c a s t C r MO s t e e l

High-alloyed steels

14% C r f o r g e d s t a i n l e s s s t e e l 167.3

15% C r N i c a s t s t a i n l e s s s t e e l 113.0

17% C r r o l l e d s t a i n l e s s s t e e l 103.0

fo rged Monel steel 26.6

c a s t S t e l l i t e s t e e l 2.1

r o l l e d S t e l l i t e s t e e l 0.9

Mousson's r e s u l t s t o g e t h e r w i t h d a t a from o t h e r

s o u r c e s a r e a v a i l a b l e i n conven ien t form i n Chap te r 9

of t h e book by Knapp e t a 1 (1970) .

Abelev e t a 1 (1971) t e s t e d samples of d i f f e r e n t s t e e l s

and p r o t e c t i v e c o a t i n g s i n v e n t u r i t u n n e l s w i t h f low

v e l o c i t i e s of up t o 60m/s. The r e s u l t s were a s

f o l l o w s :

carbon s t e e l - p i t t i n g a l l o v e r s u r f a c e

a f t e r 25 hours

s t a i n l e s s s t e e l (lX18H9T) - no e r o s i o n a f t e r 200

hours

epoxy-thiokol over carbon - upper l a y e r s damaged

s t e e l a f t e r 40 hours

rubber o v e r carbon s t e e l - s l i g h t breaking away a f t e r

100 hours

n y r i t e o v e r carbon s t e e l - s l i g h t e r o s i o n a f t e r 200

hours

Although s t e e l l i n i n g s a r e o f t e n used i n t u n n e l s

downstream of high-head g a t e s , Locher h Hsu (1984)

ment ion t h a t armouring c h u t e b l o c k s and b a f f l e b locks

i n s t i l l i n g b a s i n s h a s n o t proved s u c c e s s f u l because

of t h e d i f f i c u l t i e s of f i x i n g .

L i h Huang (1985) s t u d i e d t h e r e l a t i o n s h i p between t h e

c a v i t a t i o n r e s i s t a n c e of e i g h t d i f f e r e n t m e t a l s and

t h e i r u l t i m a t e r e s i l i e n c e . The r e s u l t s were found t o

f i t t h e fo rmula

where AV/& i s t h e r a t e of volume l o s s of t h e test

sample i n mm3/h, and Hv5 i s ( b e l i e v e d t o be) t h e

V i c k e r s Hardness of t h e m a t e r i a l , measured u s i n g a n

a p p l i e d l o a d of 5kg.

An ICOLD Committee (1986) found t h a t t h e r e were no

d e f i n i t e g u i d e l i n e s on how f a r steel l i n i n g s shou ld be

ex tended downstream of o r i f i c e s o r g a t e s . It was

s u g g e s t e d t h a t , i f t h e f low v e l o c i t y exceeds 25m/s,

s t e e l p r o t e c t i o n shou ld be p rov ided f o r t h e f o l l o w i n g

d i s t a n c e s :

f l o o r - 50 R

f u l l w e t t e d h e i g h t of s i d e w a l l s - 15 R

h a l f w e t t e d h e i g h t of s i d e w a l l s - 30 R

where R i s t h e h y d r a u l i c r a d i u s of t h e o r i f i c e o r g a t e

opening. S t e e l l i n i n g s i n f l i p b u c k e t s and s t i l l i n g

b a s i n s shou ld be w e l l d r a i n e d and t i e d back t o t h e

c o n c r e t e i n o r d e r t o resist t h e j e t t i n g a c t i o n of t h e

f low.

E . 3 Epoxy and

p o l y e s t e r

r e s i n s

A u s e f u l guide t o t h e p r o p e r t i e s and u s e s of t h e s e

r e s i n s is g i v e n by Tabor (1978). P o l y e s t e r r e s i n s

belong t o t h e group known a s a l k y d s o r g l y p t a l s , and

t h e y deve lop t h e i r s t r e n g t h by t h e fo rmat ion of

c o n n e c t i o n s between s i m i l a r molecu les . The r e a c t i o n

is i n h i b i t e d by t h e p resence of o t h e r t r a c e c h e m i c a l s ,

and i s s t a r t e d by t h e a d d i t i o n of a c a t a l y s t . The

r e s i n c a n be made e a s i e r t o use by add ing a d i l u e n t

which h a s s i m i l a r connec to r s and t h e r e f o r e t a k e s p a r t

i n t h e r e a c t i o n .

By c o n t r a s t epoxy r e s i n s c o n s i s t of two d i f f e r e n t

chemica l s w i t h "epoxide" groups which r e a c t , when

brought t o g e t h e r , t o form a s o l i d . The l i q u i d r e s i n

h a s a good a f f i n i t y f o r c o n c r e t e and s o forms a s t r o n g

bond. The amount of ha rdener needs t o be measured

a c c u r a t e l y s o a s t o e n s u r e t h a t a l l t h e r e s i n c a n be

c o n v e r t e d . The r a t e of r e a c t i o n is a f f e c t e d by

t e m p e r a t u r e , and can be i n c r e a s e d by t h e a d d i t i o n of a

chemica l a c c e l e r a t o r .

R e s i n s can be used d i r e c t l y a s a d h e s i v e s and s u r f a c e

c o a t i n g s , o r they can be mixed w i t h i n e r t m i n e r a l

f i l l e r s o r a g g r e g a t e s t o produce m o r t a r s . Epoxy and

p o l y e s t e r r e s i n s have f a i r l y s i m i l a r p r o p e r t i e s :

compress ive s t r e n g t h s abou t 2.5 t imes t h a t of p o r t l a n d

cement mortar o r c o n c r e t e ; Young's moduli

approx imate ly 0.1-0.3 t imes t h a t of c o n c r e t e ;

c o e f f i c i e n t s of the rmal expans ion abou t 3 t imes t h a t

of c o n c r e t e . Res ins a l s o t end t o c r e e p under l o a d

much more t h a n c o n v e n t i o n a l m a t e r i a l s . The p r o p e r t i e s

of r e s i n m o r t a r s can , however, be v a r i e d c o n s i d e r a b l y

by t h e c h o i c e of s u i t a b l e f i l l e r s . Some epoxy r e s i n s

may n o t c u r e i f m o i s t u r e is p r e s e n t , and s u r f a c t a n t s

must be added t o o b t a i n a bond under w a t e r . The

d e s i g n of a r e s i n o r mortar r e q u i r e s s p e c i a l i s t

knowledge, and shou ld be t a i l o r e d t o t h e needs of each

p a r t i c u l a r job. Also t h e s t a n d a r d s of c o n t r o l needed

on s i t e a r e h i g h e r than a r e normal ly encountered when

working wi th c o n v e n t i o n a l c o n c r e t e .

Refe rences i n t h e l i t e r a t u r e s u g g e s t t h a t epoxy

m a t e r i a l s have no t performed w e l l i n h y d r a u l i c

s t r u c t u r e s s u b j e c t t o h igh v e l o c i t y f lows. It i s

p o s s i b l e , however, t h a t t h e f a i l u r e s may have rece ived

more a t t e n t i o n than t h e s u c c e s s e s .

Wagner h J a b a r a (1971) r e p o r t USBR e x p e r i e n c e on s e v e n

dams which s u f f e r e d c a v i t a t i o n damage. Near ly a l l t h e

r e p a i r s c a r r i e d ou t w i t h e p o x i e s o r epoxy m o r t a r s

s u b s e q u e n t l y f a i l e d .

G a l p e r i n e t a1 (1977) d e s c r i b e t h e use of epox ies a t

Krasnoyarsk Dam (USSR) t o r e c t i f y s u r f a c e

i m p e r f e c t i o n s found a f t e r c o n s t r u c t i o n . Holes up t o

50mm deep were f i l l e d w i t h a n epoxy-based p l a s t i c mix

which performed w e l l . An epoxy-based cement mix was

used f o r h o l e s 50-100mm d e e p , but many of t h e r e p a i r s

f a i l e d and caused s e r i o u s c a v i t a t i o n e r o s i o n

downstream. Holes d e e p e r t h a n lOOmm were f i l l e d u s i n g

c o n c r e t e ( c o n t a i n i n g 5-20mm s i z e crushed rock) on a n

epoxy base. A p r o t e c t i v e l a y e r of epoxy p a i n t was

a l s o a p p l i e d t o t h e s u r f a c e of t h e s p i l l w a y bucket ;

t h i s was found t o d e l a y bu t not p reven t t h e s t a r t of

c a v i t a t i o n damage.

Examples of t h e u s e of e p o x i e s a t T a r b e l a Dam

( P a k i s t a n ) a r e g i v e n by Lowe et a 1 (1979) and Chao

(1980) . The f l o o r and a w a l l of Tunnel 3A were

r e p a i r e d w i t h o r d i n a r y c o n c r e t e f i n i s h e d w i t h a l a y e r

of epoxy c o n c r e t e . T h i s f a i l e d a f t e r t h r e e y e a r s and

was r e p l a c e d w i t h a s t e e l l i n i n g . Epoxy c o a t s were

a p p l i e d t o c o n c r e t e s u r f a c e s i n t h e s t i l l i n g b a s i n s ,

b u t f a i l e d a s a r e s u l t of poor bond. Sinmast P-103

p a s t e proved s a t i s f a c t o r y f o r r e p a i r i n g a r e a s where

t h e d e p t h of e r o s i o n d i d no t exceed 6mm. However,

where epoxy m o r t a r was used f o r d e e p e r a r e a s of

damage, t h e c o n c r e t e below t h e r e p a i r p u l l e d away f rom

i t due t o t h e d i f f e r e n t the rmal expans ions of t h e two

m a t e r i a l s . Pa tches on w a l l s exposed t o d i r e c t

s u n l i g h t f a i l e d w i t h i n a m a t t e r of days .

Problems w i t h e p o x i e s a r e a t t r i b u t e d by Warner (1980)

t o :

1. poor s u r f a c e p r e p a r a t i o n ( d i r t , w e t ) ;

2. poor mixing;

3. t o o much h e a t g e n e r a t i o n ;

4. u n s u i t a b l e f o r m u l a t i o n of epoxy;

5. f o r m u l a t i o n n o t compat ib le w i t h m o i s t u r e ( e i t h e r

p r e s e n t n a t u r a l l y o r g e n e r a t e d by h e a t ) .

A t Dworshak Dam (USA) a n a r e a of 3m2 of c o n c r e t e w a l l

was c o a t e d w i t h epoxy mortar . The c o a t i n g had t o be

a p p l i e d t h r e e t i m e s ; on t h e f i r s t o c c a s i o n t h e epoxy

was improper ly mixed, and on t h e second t h e r e was a

l a c k of bond i n wet a r e a s . A f t e r comple t ion t h e

s u r f a c e had t o be ground t o remove s a g s . Epoxy m o r t a r

was a l s o used t o r e p a i r t h e s t i l l i n g b a s i n . Bad

w e a t h e r and i n s u f f f c i e n t t ime p reven ted a s a t i s f a c t o r y

j o b ( p r e s e n c e of m o i s t u r e , poor mixing and

p r e p a r a t i o n ) . Approximately 20L of t h e epoxy m a t e r i a l

was l o s t a f t e r 53 days s e r v i c e , and 80% had gone

w i t h i n a few more months.

E.4 P l a s t i c s and Hobbs used f low p a s t a c y l i n d e r t o s t u d y t h e

o t h e r materials c a v i t a t i o n r e s i s t a n c e of p l a s t i c s and o t h e r m a t e r i a l s .

Most of t h e p l a s t i c s showed l i t t l e damage, and s o were

n o t r a t e d on t h e b a s i s of weight l o s s , bu t v i s u a l l y a s

f o l l o w s .

E x c e l l e n t monocast ny lon

ny lon 66

high-impact po ly thene

Very good "a lka thene" po ly thene

"propathene" po lypropy lene

aluminium bronze

Good n y l a t r o n GS

s t a i n l e s s s t e e l

F a i r f luorocarbon PTFE

" d a r v i c " v i n y l

h i g h - t e n s i l e b r a s s

Bad -. pen ton K51

aluminium a l l o y

Very bad perspex a c r y l i c r e s i n .

Although ny lon performed w e l l , i t h a s poor f a t i g u e

p r o p e r t i e s and a b s o r b s wa te r . Good c a v i t a t i o n

r e s i s t a n c e was found t o c o r r e l a t e i n most c a s e s w i t h a

h igh v a l u e of t h e q u a n t i t y ( t e n s i l e s t r e n g t h ) 2/

( e l a s t i c modulus); penton and perspex d i d n o t f i t t h e

p a t t e r n .

Inozemtsev e t a 1 (1965) ment ion t h a t s h e e t rubber i s

e f f e c t i v e i n p r e v e n t i n g c a v i t a t i o n damage, but t h a t no

r e l i a b l e means of f i x i n g i t h a s been d e v i s e d . Thin

c o a t i n g s of s y n t h e t i c rubber i n c r e a s e t h e l i f e of

c o n c r e t e by a f a c t o r of between 3 and 20, but t h e i r

c a v i t a t i o n r e s i s t a n c e i s s t i l l on ly 1 / 1 0 t o 1 / 2 0 t h a t

of s t e e l .

According t o Kenn (1968) t h e b e s t l i n i n g m a t e r i a l s a r e

s t a i n l e s s s t e e l , neoprene and t h i o k o l r u b b e r , and

t h e s e have b e t t e r c a v i t a t i o n - r e s i s t i n g p r o p e r t i e s t h a n

epoxy and p h e n o l i c r e s i n s .

R e s u l t s of t e s t s on some l i n i n g m a t e r i a l s c a r r i e d o u t

by Abelev e t a 1 (1971) have a l r e a d y been mentioned i n

S e c t i o n E.2.

Wagner h J a b a r a (1971) r e p o r t e d t h a t a neoprene

compound was found i n US Bureau of Reclamat ion

e x p e r i e n c e t o be t h e on ly s u i t a b l e c o a t i n g m a t e r i a l .

A t h i c k n e s s of 70mm was r e q u i r e d , and t h i s was b u i l t

up i n 2mm t h i c k l a y e r s a p p l i e d by b rush , w i t h a

w a i t i n g p e r i o d of up t o two h o u r s between each

a p p l i c a t i o n .

The c a v i t a t i o n r e s i s t a n c e of v a r i o u s po lymer ic

m a t e r i a l s was s t u d i e d by B a r l e t t a h B a l l (1983). No

c l e a r r e l a t i o n s h i p was found between r e s i s t a n c e and

any s i n g l e mechanical o r chemica l p r o p e r t y . The

performance of t h e m a t e r i a l s was r a t e d a s f o l l o w s :

Bes t he te rogeneous polymers ( eg polyamide 6.6

p l u s p o l y e t h y l e n e , and p o l y a c e t a l p l u s

p o l y e t h y l e n e )

I n t e r m e d i a t e homogeneous polymers

Worst p o l y u r e t h a n e and po lyca rbona te .

F i b r e - r e i n f o r c e d and f i b r e - f i l l e d polymers were less

r e s i s t a n t t h a n t h e homogeneous m a t r i x m a t e r i a l s

a l o n e .

R e s u l t s of a b r a s i o n t e s t s on a p o l y u r e t h a n e r e s i n

( S i k a f l e x KW2) were d e s c r i b e d i n an ICOLD (1986)

su rvey . The r e s i n was a p p l i e d a s a p r o t e c t i v e l a y e r

t o c o n c r e t e a t Rhasm e l Gi rba Dam i n t h e form of a

14mm t h i c k m o r t a r l a y e r and a n 8mm t h i c k wear ing c o a t

of t h e n e a t r e s i n . L a b o r a t o r y tests showed t h a t t h e

a b r a s i o n r e s i s t a n c e of n e a t S i k a f l e x was i n t e r m e d i a t e

between n e a t epoxy and steel; t h e e l a s t i c i t y of t h e

r e s i n may e n a b l e i t t o r e s i s t c a v i t a t i o n damage, b u t

test d a t a a r e n o t a v a i l a b l e .

APPENDIX F

A I R ENTRAINMENT

F. l E f f e c t on The p r e s e n c e of a i r i n w a t e r lowers t h e p r e s s u r e s

c a v i t a t i o n g e n e r a t e d by c o l l a p s i n g c a v i t i e s , and can t h e r e b y

reduce t h e amount of damage t h a t they cause . P e t e r k a

(1953) s t u d i e d t h i s b e n e f i c i a l e f f e c t of a i r u s i n g

c o n c r e t e samples i n a v e n t u r i t u n n e l a t f low

v e l o c i t i e s of a b o u t 30m/s. The weight l o s s due t o

e r o s i o n was approx imate ly ha lved when t h e a i r

c o n c e n t r a t i o n was C = l%, and became n e g l i g i b l e f o r

C > 7.4%. These c o n c l u s i o n s were conf i rmed by l a t e r

work by R u s s e l l 6 Sheehan (1974) and by Oskolkov 6

Semonkov (1979) who found t h a t a n a i r c o n c e n t r a t i o n o f

C = 7 4 % was s u f f i c i e n t t o p r e v e n t damage t o c o n c r e t e

a t f low v e l o c i t i e s of up t o 45mls.

Refe rence h a s a l r e a d y been made i n S e c t i o n E.l t o t h e

d a t a p r e s e n t e d by G a l p e r i n et a 1 (1971) and Kudriashov

e t a 1 (1983) on a l l o w a b l e f low v e l o c i t i e s f o r

c o n c r e t e . T e s t s were a l s o c a r r i e d o u t t o d e t e r m i n e

how t h e amount of a i r p a f f e c t s t h e a l l o w a b l e

v e l o c i t y , where i s d e f i n e d a s :

and Q i s t h e f low r a t e of a i r and Q t h a t of t h e a W

w a t e r . The r e s u l t s of b o t h s t u d i e s can b e

approximated by Equa t ion ( E ) b u t co r respond t o

d i f f e r e n t v a l u e s of t h e c o n s t a n t U, a s f o l l o w s :

Amount of A i r Cons tan t U (m/s)

B(%) G a l p e r i n (1971) Kudriashov (1983)

Vorobiyov (1983) found that the volume of cavitation

erosion was reduced by a factor y which varied with

the air concentration C ( % ) as

A theoretical description of the effect of air on

collapsing cavities was provided by Huang et a1

(1985). The model reproduces the unsymmetrical

collapse of cavities near solid boundaries, and shows

that entrained air reduces the peak pressures by

decreasing the speed of sound in the liquid.

Air tends to be entrained naturally at the surface of

a high velocity flow and becomes dispersed through the

depth by turbulent mixing. The above results indicate

that cavitation damage may be prevented if the

resulting air concentration at the bed reaches a value

of about 7%. It is therefore important to be able to

predict the amount and distribution of air entrained

by flow on a spillway. If there is insufficient

natural entrainment to prevent cavitation, it is

possible to add air to the flow by means of aerators

constructed in the floor and walls of the channel or

tunnel.

An important factor affecting self-aeration and also

the performance of aerators is the rise velocity of

air bubbles in water. Data from various sources are

summarised by McKeogh et a1 (1983) as follows

1

vb = ((0.01 rb)+(0.079/rb) 1' , lmm S r 5 5mm (F.3b)

b

where V is the rise velocity in m/s and r is the b b

radius of the bubble in mm.

F.2 Self-aeration Air concentration can be defined in terms of the

volumes of air and water, ie

or in terms of their flow rates, ie

The two definitions are compatible only if the air and

water travel at the same velocity (speed and

direction). This is a reasonable assumption if the

bubbles are small enough for their slip velocity and

rise velocity to be small compared with that of the

fluid. The choice of definition is usually determined

by the experimental technique used to measure the

concentration: Equation F.4 would be appropriate for

a device that measures the size and number of bubbles

in a given volume; Equation F.5 would be suitable

where the total rates of air and water supply are

known. The symbol C will be used in cases where the

concentration is not defined precisely. Results for

aerators are sometimes presented in terms of the ratio

pin Equation F.l; clearly at low concentrations f3

and C are nearly equal. A separate problem of 2

definition occurs where a turbulent water surface

causes an instrument to be periodically in and out of

the flow; in these conditions it may be difficult to

determine what proportion of a measurement is due to

air bubbles in water and what is due to air above the

free surface.

There is general agreement that air entrainment on a

spillway starts when the boundary layer grows

sufficiently for its thickness 6 to be nearly equal to

the depth of flow d. Turbulent clumps of liquid then

break through the free surface and fall back again,

thereby entraining air. The distance along the

channel required for this to occur is called the

inception length Li; some authors assume that at the

point of inception d = 6. while others assume d = 1.26

since turbulent eddies can be projected from below the

free surface. Downstream of the point of inception

three zones can be defined. In the "developing

partially-aerated zone" the mechanism of turbulent

diffusion causes some of the entrained air to spread

downwards as it is carried along by the flow. When

air becomes present at the bed, the flow enters the

"developing fully-aerated zone" in which the depth of

water, the amount of air and its distribution pattern

within the flow all continue to vary with distance.

Finally, if the channel is long enough and of constant

slope, the flow reaches the "uniform aerated zone"

where there is no further change in depth or in the

vertical profile of air concentration.

A large amount of research has been carried out on

self-aeration, and in this review it is appropriate to

concentrate mainly on the more recent work. A classic

series of experiments on air entrainment in a rough

channel was performed by Straub 6 Anderson (1958),

while Anderson (1965) gives corresponding results for

a smooth channel. Tests were conducted in a 15.2m

long flume with unit discharges up to 0.9rn3/s/rn and

slopes up to 75'. Measurements were made to determine

the mean concentration of the air and its distribution

with depth for conditions of uniform aerated flow.

Below a certain transition depth d it was found that T the flow consisted mainly of air bubbles in water,

while above this depth it was predominantly water

droplets in air; d was identified as the point where T

the rate of change of local air concentration with

depth (dC/dy) was maximum. The measured air

distributions above and below d were able to be T

fitted to two separate theoretical equations by

choosing suitable values of certain coefficients.

Based on these and other data, an ASCE Task Committee

(1961) recommended the following formula for

predicting the mean air concentration (averaged over

depth) in rough channels.

- Cl = 0.743 log (sin8/qli5) + 0.723

10 (F-6)

where Ois the angle of the channel to the horizontal

and q is the unit discharge in m3/s/m. The

corresponding result for flow in a smooth channel was

found by Anderson to be

Values of the Darcy-Weisbach friction factor h were

calculated from the equation:

where d is the transition depth defined previously T

and is the mean velocity of the water such that:

Here, d is the equivalent water depth calculated e

from:

On t h i s b a s i s , i t was found t h a t a i r e n t r a i n m e n t d i d

no t a l t e r t h e f low r e s i s t a n c e of t h e rough channe l

( A = 0.0315), bu t d i d reduce t h a t of t h e smooth

c h a n n e l from A = 0.0204 t o A = 0.0110.

A s e r i e s of f a i r l y s i m i l a r exper iments was c a r r i e d o u t

by Lakshmana Rao e t a 1 (1970) , Gangadhariah e t a 1

(1970) and Lakshmana Rao 6 Gangadhariah (1971) , a

summary of which i s g iven by Lakshmana Rao 6 Kobus.

The d a t a on t h e v a r i a t i o n of a i r c o n c e n t r a t i o n w i t h

d e p t h were f i t t e d t o d i f f e r e n t t h e o r e t i c a l e q u a t i o n s

from t h o s e used by S t r a u b 6 Anderson ( s e e above) , b u t

a g a i n i t was n e c e s s a r y t o choose s u i t a b l e v a l u e s f o r

c e r t a i n c o e f f i c i e n t s . For t h e i n c e p t i o n of a i r

e n t r a i n m e n t , i t was sugges ted t h a t i n a d d i t i o n t o t h e

boundary l a y e r r e a c h i n g t h e s u r f a c e , i t i s n e c e s s a r y

f o r t h e t u r b u l e n t f l u c t u a t i o n s t o have s u f f i c i e n t

ene rgy t o overcome t h e f o r c e of s u r f a c e t e n s i o n ; t h e

c r i t e r i o n f o r t h i s was found t o be

where V is t h e a v e r a g e f low v e l o c i t y , V, t h e s h e a r

v e l o c i t y a t t h e bed and 6 t h e s u r f a c e t e n s i o n . The

f o l l o w i n g e q u a t i o n was o b t a i n e d f o r t h e mean a i r

c o n c e n t r a t i o n i n uniform a e r a t e d f l o w

(F. 12)

where t h e e q u i v a l e n t Froude number F i s d e f i n e d a s e

a n d and d a r e r e s p e c t i v e l y t h e mean v e l o c i t y and e

e q u i v a l e n t w a t e r d e p t h c a l c u l a t e d from Equa t ions F.9

and F.lO. The c o e f f i c i e n t Q is g iven by:

Q = 1.35n f o r r e c t a n g u l a r c h a n n e l s (F .14a)

Q = 2.16n f o r t r a p e z o i d a l c h a n n e l s (F.14b)

w i t h n b e i n g t h e Manning roughness c o e f f i c i e n t of t h e

channe l . I n t h e e x p e r i m e n t s , v a l u e s of n f o r a e r a t e d

f l o w s were de te rmined from a n ana logue of Equa t ion F.8

used by S t r a u b & Anderson, i e :

A p p l i c a t i o n of E q u a t i o n F.12 t o f i n d C i n a d e s i g n

s i t u a t i o n i s n o t s t r a i g h t f o r w a r d because v a l u e s of d e '

V and p o s s i b l y n need t o be found f i r s t .

The p o s i t i o n of t h e c r i t i c a l p o i n t a t which a i r

e n t r a i n m e n t s t a r t s depends on t h e u n i t d i s c h a r g e .

G a l p e r i n e t a 1 (1977) g i v e t h e f o l l o w i n g f i e l d d a t a

f o r high-head s p i l l w a y s :

U n i t d i s c h a r g e D i s t a n c e from s p i l l w a y (m 3/s/m) c r e s t (m)

O b s e r v a t i o n s a t B r a t s k and Krasnoyarsk Dams (USSR)

showed t h a t a r e a s which were e roded when t h e f low was

n o t a e r a t e d d i d n o t s u f f e r damage a t lower f l o w s when

t h e f low was s e l f - a e r a t e d .

Thandaveswara & Lakshmana Rao (1978) s t u d i e d t h e

r e g i o n of deve lop ing a e r a t i o n , between t h e p o i n t of

inception and the establishment of uniform flow, using

a channel with unit discharges of up to 0.20m3/s/m and

slopes between 15.3" and 30.7'. The measurements

indicated that in the developing fully-aerated zone

(see above) the air concentration reached a minimum

above the bed and not at the bed as other researchers

have found. If this finding were confirmed, it would

be significant when determining whether the air

concentration on the floor of a channel is sufficient

to prevent cavitation damage.

Falvey (1979, 1980) correlated Straub & Anderson's

data with measurements from four prototype structures

(three chutes and one spillway) to obtain the

following equation for the mean air concentration in

uniform aerated flow

where the Froude number is given by:

and the Weber number by:

The length dimension L is not precisely defined in W

these references, and it is unclear whether it should

be the flow depth, the hydraulic depth (area/surface

width), or the hydraulic radius (area/wetted

perimeter). The values of V and L are calculated as W W

though the flow were not aerated. Although the

surface tension awas included in che correlation, its

value is likely to have been approximately constant

within the data set used. Air entrainment leads to

bulking of the flow, and the depth for design is

sometimes assumed to be equal to dw/(l-C). However,

Falvey (1979) points out that it is not a very useful

parameter, because turbulence causes water to rise

well above this level.

Wang (1981) used experimental data on mean air

concentrations to compare the predictions of six

existing formulae, but found that the minimum standard

deviation was given by a new equation

where Fr - vw

-7 ( gRw)

B is the width of the channel, and the depth d and W

the hydraulic radius R are calculated assuming W

non-aerated flow.

Volkart (1982) studied air entrainment in steep

partially-filled pipes, and obtained both model and

prototype data for pipe diameters up to 900mm and

slopes up to 4 5 ' . The resulting equation for the mean

air concentration was

where F is calculated from Equation F.20 using the r

non-aerated flow parameters. The mean velocity V of aw the air-water mixture was given by

The area of flow A corresponding to the maximum m

height h reached occasionally by the aerated water m

surface was related to the non-aerated flow area A W

by

To prevent slug flow occurring in a pipe it was

recommended that h /D < 0.9. m

Bruschin (1982) compared Falvey's Equation F.16 and

Volkart's Equation F.21 for mean air concentration,

and concluded that Equation F.16 did not give

reasonable predictions for prototype conditions,

possibly due to the second term on the right-hand side

not being valid.

Wang (1984) used measured data on mean air

concentrations to obtain the following best-fit

equation.

where n is the Manning roughness of the channel.

An important line of research on air entrainment has

stemmed from prototype measurements carried out by

Cain & Wood (1981 a,b) on Aviemore Dam (New Zealand).

Instruments were developed to determine profiles of

air concentration and water velocity along the

spillway and also the size of the air bubbles. The

spillway slope is 4 5 " , and data were obtained for unit

discharges of up to 3.15m3/s/m; the channel was not

long enough to give conditions of uniform aerated

flow. Measurements of the point of inception of air

entrainment were found to correspond reasonably with

t h e e m p i r i c a l e q u a t i o n due t o Bauer (1954) f o r t h e

growth of t h e boundary l a y e r t h i c k n e s s

where k i s t h e e q u i v a l e n t sand roughness of t h e S

c h a n n e l . Downstream of t h e p o i n t of i n c e p t i o n i t was

found t h a t t h e non-dimensional v e l o c i t y p r o f i l e d i d

no t va ry w i t h t h e amount of e n t r a i n e d a i r , and had t h e

form

where t h e s u b s c r i p t 90 r e f e r s t o t h e p o i n t above t h e

bed where t h e a i r c o n c e n t r a t i o n i s 90%. T h i s

c o n t r a d i c t s t h e r e s u l t s of o t h e r i n v e s t i g a t o r s ( e g ,

S t r a u b h Anderson, Lakshmana Rao e t a l , s e e above) who

found t h a t t h e v e l o c i t y d i d n o t i n c r e a s e s t e a d i l y w i t h

l e v e l , but reached a maximum below t h e s u r f a c e of t h e

f low. Cain h Wood sugges t t h a t t h e d i f f e r e n c e a r i s e s

because they measured t h e v e l o c i t y of t h e w a t e r w h i l e

o t h e r i n v e s t i g a t o r s measured t h a t of t h e a i r - w a t e r

mix ture ; i f t h i s is t h e c a s e i t s u g g e s t s t h a t t h e two

phases t r a v e l a t s i g n i f i c a n t l y d i f f e r e n t s p e e d s ,

c o n t r a r y t o what i s o f t e n assumed.

D i s c r e p a n c i e s such a s t h e s e between d i f f e r e n t s t u d i e s

may be due t o t h e measuring i n s t r u m e n t s having

d i f f e r e n t o p e r a t i n g p r i n c i p l e s . Most measurements o f

t h e v e l o c i t y and c o n c e n t r a t i o n of a e r a t e d f lows a r e

i n d i r e c t , and t h e r e s u l t s may n o t t h e r e f o r e be e x a c t l y

comparable. D e t a i l s of some of t h e s e i n s t r u m e n t s a r e

g i v e n i n S e c t i o n G.3.

Wood e t a 1 (1983) assumed t h a t t h e formula f o r t h e

growth of a boundary l a y e r was s i m i l a r i n form t o

B a u e r ' s Equa t ion F . 2 5 , but e v a l u a t e d t h e c o e f f i c i e n t s

u s i n g Equa t ion F.26 t o g e t h e r wi th numer ica l r e s u l t s

o b t a i n e d by K e l l e r h Ras tog i (1977) Eor t h e p o i n t of

i n c e p t i o n on s t a n d a r d s p i l l w a y s . T h i s procedure gave

where H i s t h e v e r t i c a l d i s t a n c e from t h e ups t ream S

t o t a l energy l i n e t o t h e s u r f a c e of t h e wa te r i n t h e

s p i l l w a y . The form of t h e e q u a t i o n a l l o w s i t t o be

a p p l i e d t o c h a n n e l s of non-uniform s l o p e .

Wood (1983) re-analysed S t r a u b h Anderson's d a t a , and

concluded t h a t uni form a e r a t e d f low was n o t i n f a c t

ach ieved i n a l l t h e t e s t s . Where e q u i l i b r i u m

c o n d i t i o n s were reached , Wood found t h a t t h e mean a i r

c o n c e n t r a t i o n and t h e d i s t r i b u t i o n of t h e a i r through

t h e d e p t h of t h e f low were u n i q u e l y determined by t h e

s l o p e of t h e channel . The v a r i a t i o n of E with c h a n n e l

s l o p e was a s f o l l o w s :

- Slope C

The d a t a a l s o i n d i c a t e t h a t i n o r d e r t o o b t a i n a l o c a l

a i r c o n c e n t r a t i o n a t t h e bed of abou t 7 % ( s o a s t o

avo id c a v i t a t i o n damage), t h e mean a i r c o n c e n t r a t i o n

needs t o be about 30% and t h e s l o p e of t h e channe l

abou t 22.5". T h i s r e s u l t a p p l i e s on ly a f t e r t h e f low

h a s t r a v e l l e d s u f f i c i e n t l y f a r a l o n g t h e channe l f o r

un i fo rm c o n d i t i o n s t o be a t t a i n e d . Upstream, i n t h e

r e g i o n of deve lop ing a e r a t e d f low, t h e a i r

concentration at the bed will be lower than the final

equilibrium value.

Wood (1985) demonstrates how results from his earlier

work can be used to produce a numerical model for

predicting air concentrations along the length of a

spillway. The point of inception is identified by

assuming that entrainment starts when the depth of

flow is equal to 1.2 times the thickness of the

boundary layer. The entrainment of air into the flow

is described in terms of a net entrainment velocity V e

where

- - Ve = (Ce - C) Vb cos El (F. 29)

Here C is the equilibrium mean air concentration for e -

the given spillway slope, C is the local value of the

mean concentration, and V is the rise velocity of the b

air bubbles. Calibration of this model against Cain h

Wood's data (see above) indicated a value for the rise

velocity of V = 0.17m/s. The development of the b

aerated flow along the spillway is then determined

using the gradually-varied flow equation and

information on the effect of air on channel roughness

obtained from a re-analysis of Straub & Anderson's

results. As mentioned above, Straub & Anderson used

Equation F.8 to determine values of the friction

factor h, and found that air entrainment did not

appear to alter the resistance of their rough channel.

Wood calculated values of h from the alternative

formula

where d is the equivalent water depth given by e

Equation F.lO. On this basis (which appears more

logical), it was found that the presence of air

reduced the flow resistance.

Ackers & Priestley (1985) developed a model for

predicting air entrainment on spillways which is based

on the same information as used by Wood (1985), but

with some detailed differences in approach. The point

of inception is found numerically by computing the

growth of the boundary layer until its thickness is

equal to the depth of flow. The effect of air

concentration on flow resistance was evaluated from

Straub & Anderson's data (using the same method as

Wood) and expressed in the form

where h and h are the friction factors for aerated a W

and non-aerated flow respectively. The change in mean

air concentration in the region of developing aeration

is calculated from the gradually-varied flow equation

and the continuity relation

This differs from Wood's Equation F.28; the definition

of concentration in Equation F.5 shows that F.33 is

correct.

The net entrainment velocity V of the air was assumed e

to be given by

' in ve = V b {(+ - C cos o} b

where V i s t h e v o l u m e t r i c r a t e a t which a i r i s i n

e n t r a i n e d i n t o t h e f low per u n i t s u r f a c e a r e a , and

V C c o s 0 i s t h e c o r r e s p o n d i n g r a t e a t which a i r b

e s c a p e s due t o i t s buoyancy (c f Equat ion F.29). Two

h y p o t h e s e s were c o n s i d e r e d f o r t h e q u a n t i t y (V /V ) : i n b

e i t h e r t h a t i t depended on ly on t h e s l o p e of t h e

c h a n n e l o r on ly on t h e v a l u e of t h e l o c a l Froude

number; comparison w i t h some of S t r a u b S Anderson 's

d a t a s u g g e s t e d t h a t t h e second h y p o t h e s i s was s l i g h t l y

s u p e r i o r .

An e q u a t i o n Eor e s t i m a t i n g t h e p o i n t of i n c e p t i o n of

a i r e n t r a i n m e n t on a s p i l l w a y c a n be o b t a i n e d by u s i n g

Equa t ion F.25 Eor t h e v e l o c i t y d i s t r i b u t i o n i n t h e

boundary l a y e r , and by assuming t h a t i n c e p t i o n o c c u r s

when t h e d e p t h of f low i s j u s t e q u a l t o t h e t h i c k n e s s

of t h e boundary l a y e r . Combining w i t h Equa t ion F.27

then g i v e s t h e f o l l o w i n g r e s u l t f o r t h e d i s t a n c e L i

(measured a l o n g t h e s p i l l w a y ) from t h e c r e s t t o t h e

p o i n t of i n c e p t i o n .

With minor d i f f e r e n c e s i n t h e c o e f f i c i e n t s , t h i s

e q u a t i o n i s e q u i v a l e n t t o one which Wood (1985)

s i m i l a r l y o b t a i n e d f o r s p i l l w a y s of c o n s t a n t s l o p e ;

t h e d e r i v a t i o n of E q u a t i o n F.35 s u g g e s t s t h a t t h e

l a t t e r may a l s o be v a l i d f o r c a s e s of v a r y i n g s l o p e .

Comparison of E q u a t i o n F.35 w i t h t h e p r o t o t y p e

measurements of L g i v e n by G a l p e r i n e t a 1 (1977). s e e i

above , shows r e a s o n a b l e q u a l i t a t i v e agreement. A

q u a n t i t a t i v e comparison cannot be made because t h e

s l o p e of t h e p r o t o t y p e s p i l l w a y was n o t s t a t e d ; t h e

e q u a t i o n would f i t t h e d a t a w e l l if t h e s l o p e were

abou t 26' and t h e s u r f a c e roughness were k = l m m . I t S

can be s e e n from Equa t ion F.35 t h a t t h e i n c e p t i o n

l e n g t h i s no t ve ry s e n s i t i v e t o changes i n roughness .

P . 3 A e r a t o r s on A e r a t o r s a r e being i n c r e a s i n g l y used t o p r o t e c t t h e

s p i l l w a y s s p i l l w a y s of high-head dams from c a v i t a t i o n damage.

T h e i r use i s a p p r o p r i a t e where t h e s t a n d a r d s of

s u r f a c e f i n i s h needed t o avoid c a v i t a t i o n a r e t o o h i g h

t o be a c h i e v a b l e and t h e r e i s i n s u f f i c i e n t e n t r a i n e d

a i r i n t h e f low t o p r e v e n t e r o s i o n by c o l l a p s i n g

c a v i t i e s .

A i r can be i n j e c t e d by means of pumps, b u t most

a e r a t o r s work by producing a r e g i o n of sub-atmospher ic

p r e s s u r e which draws a i r n a t u r a l l y i n t o t h e f low.

T h i s i s ach ieved by means of a ramp, s l o t o r o f f s e t

which c a u s e s t h e f low t o s e p a r a t e from p a r t of t h e

boundary and form a s t a b l e pocket of a i r .

Requirements of a n e f f e c t i v e a e r a t i o n sys tem a r e

t h a t :

1. I t s a i r demand shou ld be s u f f i c i e n t t o g i v e

l o c a l a i r c o n c e n t r a t i o n s a t t h e boundar ies

t h a t a r e h i g h enough t o p reven t c a v i t a t i o n

damage ( t y p i c a l l y C > 7 % ) ;

2. The a i r c a v i t y produced by t h e d e v i c e s h o u l d

remain s t a b l e over t h e f u l l r ange of

o p e r a t i n g c o n d i t i o n s and should no t tend t o

f i l l w i t h wa te r ;

3. The a e r a t o r should no t produce t o o g r e a t a

d i s t u r b a n c e of t h e f low o r a n e x c e s s i v e

amount of s p r a y ;

4. The s p a c i n g between s u c c e s s i v e a e r a t o r s

should be such t h a t t h e l o c a l a i r

c o n c e n t r a t i o n a t t h e f l o o r does n o t f a l l

below t h e amount r e q u i r e d t o p r o v i d e

p r o t e c t i o n a g a i n s t c a v i t a t i o n damage.

The a i r demand depends upon t h e v e l o c i t y and d e p t h of

t h e w a t e r , and upon t h e geometry of t h e a e r a t o r and

t h e sys tem of d u c t i n g which s u p p l i e s i t w i t h a i r .

Model tests a r e u s u a l l y c a r r i e d o u t t o s t u d y t h e

behaviour of t h e f low around a n a e r a t o r . The

phenomenon of a i r e n t r a i n m e n t i s s u b j e c t t o

s i g n i f i c a n t s c a l e e f f e c t s , s o s m a l l models c a n n o t

normal ly p rov ide a c c u r a t e p r e d i c t i o n s of a i r demand.

An a e r a t o r i n i t i a l l y produces a h i g h c o n c e n t r a t i o n of

a i r n e a r t h e boundary, b u t t h e d i s t r i b u t i o n becomes

more un i fo rm a s t h e bubbles a r e c a r r i e d downstream by

t h e f low. The t r a n s v e r s e movement of t h e a i r i s

de te rmined by two e f f e c t s : t u r b u l e n t d i f f u s i o n away

f rom a r e a s of h i g h c o n c e n t r a t i o n , and buoyancy f o r c e s

due t o p r e s s u r e g r a d i e n t s . G r a v i t y g i v e s rise t o a n

upward-di rected buoyancy f o r c e , bu t t h i s may be

c o u n t e r a c t e d by t h e e f f e c t s of f low c u r v a t u r e .

A e r a t o r s can c o n s i s t of d e f l e c t o r s , o f f s e t s , n o t c h e s

o r s l o t s used e i t h e r s i n g l y o r i n combinat ion; t h e

e l e m e n t s of some t y p i c a l d e s i g n s a r e shown i n F i g u r e

8. Means of s u p p l y i n g a i r t o a n a e r a t o r a r e shown i n

F i g u r e 9 and i n c l u d e :

1. u s e of a s e p a r a t i o n zone formed downstream

of a p i e r o r d i v i d e w a l l ;

2. o f f s e t s o r d e f l e c t o r s a t t h e s i d e w a l l s

which a l l o w a f l o w of a i r from t h e s u r f a c e

t o t h e f l o o r of t h e channe l ;

3. ducts discharging air at the base of the

side walls;

4. a duct beneath the floor of the channel

connecting to a horizontal slot or to the

downstream face of a vertical offset.

The design of each aeration system tends to be

specific to the particular application, and data on

some prototype installations (built or planned) are

given in Table 3.

Hay & White (1975) tested two types of aerator as part

of a more general model atudy to determine whether

aeration would increase the efficiency of stilling

basins, and reduce the amount of scour in downstream

erodible channels. The first type consisted of a

number of individual aerators, each of which comprised

a small semi-circular notch in the spillway surface

with a tear-shaped deflector upstream. A double row

of this design of aerator gave mean air concentrations -

of up to C - = 15%. The second type consisted of a

continuous slot acroas the spillway with downstream a

large-radius transition to the smooth profile of the

channel; this produced values of up to C = 25%.

Adding air to the flow gave more stable conditions in

the stilling basin and reduced the amount of

downstream scour for basins of simple design (but not

for the more complicated USBR Type 111).

According to Oskolkov & Semenkov (1979) the height of

offset needed to produce an adequate length of air

cavity is typically in the range 1.5 - 2.5~. but can be up to 5-7m; an advantage of offsets is that they

produce relatively little flow disturbance.

Deflectors produce stronger aeration than offsets, and

normally need to be only about 0.1 - 0.810 high. These

suggested sizes of offsets and deflec~ors are larger

t h a n have been used i n most p r o t o t y p e i n s t a l l a t i o n s

( s e e Tab le 3) .

Prusza e t a 1 (1983) g i v e recommendations on t h e d e s i g n

of a e r a t o r s based on Russ ian e x p e r i e n c e and work

c a r r i e d o u t f o r Guri Dam (Venezuela) . An a e r a t o r

needs t o produce l o c a l a i r c o n c e n t r a t i o n s of more than

7-8% i n a 150-200mm t h i c k l a y e r a d j a c e n t t o t h e f l o o r

and w a l l s of a channel . I n o r d e r t o p reven t

a t o m i s a t i o n of t h e f l o w t h e mean a i r c o n c e n t r a t i o n

s h o u l d n o t exceed C = 40-50%; a t t h i s l i m i t t h e l e n g t h

of c a v i t y produced by t h e a e r a t o r w i l l be a b o u t 3-5

t imes t h e d e p t h of f low. A t low d i s c h a r g e s t h e l e n g t h

of a i r c a v i t y ought no t t o be more t h a n 20-25% of i t s

l e n g t h a t t h e maximum d i s c h a r g e . I f a ramp is used on

a concave s u r f a c e , t h e r e must be a s t r a i g h t l e n g t h of

channe l upst ream of t h e a e r a t o r e q u a l t o a t l e a s t 3

times t h e d e p t h of f low. A s t h e v e l o c i t y of f low on a

s p i l l w a y i n c r e a s e s , t h e r e q u i r e d h e i g h t and a n g l e of

ramp bo th d e c r e a s e . I f a i r i s s u p p l i e d v i a a g a l l e r y ,

e i t h e r a n o f f s e t o r a n o f f s e t w i t h a ramp i s

recommended; t h e t o t a l c r o s s - s e c t i o n a l a r e a of t h e

o u t l e t s of t h e a i r d u c t s shou ld n o t be less t h a n t h a t

of t h e g a l l e r y . I f a l a r g e r f low of a i r i s needed,

t h i s i s b e s t ach ieved by means of a d d i t i o n a l

d e f l e c t o r s i n t h e s i d e w a l l s ; t h e s e a r e c a p a b l e of

p r o v i d i n g a t r a n s v e r s e supp ly of a i r i n c h a n n e l s up t o

50m wide. For a l l types of a e r a t o r s i t may be

n e c e s s a r y t o add c o r n e r wedges a t t h e j u n c t i o n s of t h e

w a l l s and t h e f l o o r s o a s t o promote a c l e a n f low

s e p a r a t i o n and reduce t h e amount of s u r f a c e

d i s t u r b a n c e .

P i n t o & Neider t (1983b) s t u d i e d t h e d i s t r i b u t i o n of

p r e s s u r e i n t h e f low a t a ramp a e r a t o r . Regions of

h igh p r e s s u r e o c c u r r e d on t h e s u r f a c e of t h e ramp (due

t o t h e c u r v a t u r e of t h e f low) and a t t h e p o i n t where

t h e s e p a r a t e d j e t r e a t t a c h e d t o t h e f l o o r of t h e

channe l . The r a p i d v a r i a t i o n s i n l o n g i t u d i n a l

p r e s s u r e induced t u r b u l e n c e i n t h e f low which

e n t r a i n e d a i r on t h e u n d e r s i d e of t h e s e p a r a t e d j e t

and a l s o a t t h e f r e e s u r f a c e . The r i s e i n p r e s s u r e a t

t h e rea t t achment p o i n t caused t h e a i r t o move upwards

from t h e f l o o r of t h e channe l . Volkar t h Chervet

(1983) found t h a t t h i s e f f e c t could reduce t h e l o c a l

a i r c o n c e n t r a t i o n a t t h e bed t o l e s s t h a n 10%, b u t t h e

accompanying r i s e i n p r e s s u r e was s u f f i c i e n t t o

p r e v e n t c a v i t a t i o n . Immediately downstream of t h e

r e a t t a c h m e n t zone, t h e a i r c o n c e n t r a t i o n a t t h e f l o o r

i n c r e a s e d r a p i d l y due t o t u r b u l e n t mixing of t h e

e n t r a i n e d a i r .

Model t e s t s on s e v e r a l types of a e r a t o r were c a r r i e d

o u t by Volkar t h Chervet (1983) f o r San Roque Dam

( P h i l l i p i n e s ) . The b e s t r e s u l t s were o b t a i n e d w i t h a

p l a i n d e f l e c t o r o r a s m a l l e r d e f l e c t o r p l u s o f f s e t . A

ramp combined w i t h a s l o t ( s e e F i g 8 c ) was n o t

s u c c e s s f u l because f a l l i n g d r o p l e t s caused t h e s l o t t o

f i l l w i t h wa te r ; t h e a d d i t i o n of d r a i n a g e h o l e s f a i l e d

t o s o l v e t h e problem. O f f s e t s a l o n e d i d no t produce a

s t r o n g enough a i r demand.

Volkar t h Rutschmann (1984a) mention t h a t a l t h o u g h

p l a i n d e f l e c t o r s can produce a good l e n g t h of a i r

c a v i t y , they tend t o work s a t i s f a c t o r i l y f o r on ly a

l i m i t e d range of f lows . A combined d e f l e c t o r and

o f f s e t was c o n s i d e r e d t o g i v e t h e b e s t r e s u l t s .

The e f f i c i e n c y of a n a e r a t o r can be i n c r e a s e d by u s i n g

" t u r b u l i s e r s " t o b reak up t h e f low p a s s i n g over a n a i r

c a v i t y . For an o f f s e t , G a l p e r i n e t a 1 (1977)

recommended t h e u s e of a n upst ream d e f l e c t o r w i t h

t r i a n g u l a r s l o t s a r r a n g e d t o produce a t r a n s v e r s e

saw-tooth p a t t e r n ; t h e h e i g h t of t h e t e e t h shou ld be

1/10 of t h e t h i c k n e s s of t h e boundary l a y e r , and t h e i r

t r a n s v e r s e s p a c i n g shou ld be a t l e a s t 1.5 t imes t h e i r

h e i g h t . Model tests showed t h a t such a d e v i c e

i n c r e a s e d t h e amount of e n t r a i n e d a i r by up t o 20%.

The l e n g t h of a i r c a v i t y produced by a n a e r a t o r i s a n

imporcanc f a c t o r affecting i c s performance. S e v e r a l

t h e o r e t i c a l methods of p r e d i c t i n g t h i s l e n g t h have

been developed by assuming t h e f low t o be

i r r o t a t i o n a l . Schwarz S Nut t (1963) s t u d i e d t h e

t r a j e c t o r y of f a l l i n g nappes , b u t t h e r e s u l t s can be

a p p l i e d t o j e t s formed by d e f l e c t o r s o r o f f s e t s ;

e q u a t i o n s f o r t h e h o r i z o n t a l and v e r t i c a l c o - o r d i n a t e s

a r e g i v e n s e p a r a t e l y , w i t h t h e t ime of t r a v e l a s t h e

common parameter . It i s assumed t h a t t h e i n i t i a l

v e l o c i t y and a n g l e of p r o j e c t i o n a r e known, and t h a t

t h e t h i c k n e s s of t h e nappe i s s m a l l s o t h a t i t behaves

e f f e c t i v e l y a s a s o l i d j e t of l i q u i d . Account i s

t a k e n of g r a v i t y and any p r e s s u r e d i f f e r e n c e between

t h e upper and lower s u r f a c e s of t h e nappe. E f f e c t s of

s u r f a c e t e n s i o n and a i r r e s i s t a n c e a r e n o t i n c l u d e d .

Pan e t a 1 (1980) de te rmined t h e t r a j e c t o r y of a s o l i d

j e t downstream of a deflector, b u t t h e s o l u t i o n does

n o t t a k e accoun t of any p r e s s u r e d i f f e r e n c e between

t h e upper and lower s u r f a c e s . Three c o r r e c c i o n

f a c c o r s were i n t r o d u c e d i n t o t h e e q u a t i o n s . The f i r s t

a l l o w s f o r t h e f a c t t h a t i n t e r n a l p r e s s u r e s i n a j e t

c a u s e t h e a n g l e a t which f l o w s e p a r a t e s from a ramp t o

be l e s s than t h a t of t h e ramp i t s e l f ; t h e r e d u c c i o n i n

a n g l e was found t h e o r e t i c a l l y u s i n g t h e method of

conformal t r a n s f o r m a t i o n ( i g n o r i n g g r a v i t y ) . The two

o t h e r f a c t o r s were de te rmined from a comparison w i t h

e x p e r i m e n t a l d a t a , and t a k e a c c o u n t of t h e e f f e c t s of

ene rgy l o s s e s and a i r r e s i s t a n c e .

Wei S De F a z i o (1982) and De F a z i o S Wei (1983) s o l v e d

L a p l a c e ' s e q u a t i o n n u m e r i c a l l y by t h e f i n i t e e lement

method t o f i n d t h e l e n g t h of c a v i t y downstream of a n

a e r a t o r . The f low upst ream of t h e ramp i s assumed C O

be uniform, but allowance can be made for curvature of

the spillway surface and differences in pressure

across the jec. Comparison wich model and prototype

data for Guri Dam showed reasonable agreement.

Yen et a1 (1984) determined the flow around aerators

by solving Laplace's equation numerically uslng three

different models based on (i) the two-dimensional

finite element method (FEM). (ii) the three-

dimensional FEM, and (iii) the two-dimensional

boundary-integral equation method (BIEM). In each

case allowance could be made for a pressure difference

across the nappe, but the shape of the lower surface

was assumed to be a parabolic curve. Results were

compared with data from a model of a deflector in a

circular tunnel. The 2-D BIEM model was the least

accurate and the 3-D FEM was slightly superior to the

2-D version. All three models overestimated the

length of the cavity by a factor of about 1.8.

Shi et a1 (1983) carried out experiments with

different heights of deflector to measure the

trajectory of the jet, the pressure pattern on the

channel floor, and the amount and distribution of air

entrained into the flow. The following regression

equation was obtained for the cavity length L c'

defined as the distance between the end of the ramp

and the point on the floor where the local air

concentration reach 60%,

where

l

v X = -p

(h Jd)'

I ' cos 0 cos ar (gd)=

and V and d a r e t h e v e l o c i t y and d e p t h of f low

upst ream of t h e a e r a t o r ; t h e o t h e r q u a n t i t i e s a r e

d e f i n e d i n F i g u r e 8 ( n o t e t h a t h l i s measured normal

t o t h e c h a n n e l , whereas h i s measured v e r t i c a l l y ) .

Wood (1985) ment ions a method used by Tan (1984) t o

e s t i m a t e t h e c a v i t y l e n g t h produced by a n o f f s e t , bu t

t h e l a t t e r r e f e r e n c e h a s n o t been s t u d i e d f o r t h i s

review.

P r e d i c t i n g t h e a i r demand is t h e most i m p o r t a n t and

t h e most d i f f i c u l t a s p e c t of d e s i g n i n g a n a e r a t o r .

Model and p r o t o t y p e s t u d i e s c a r r i e d o u t by P i n t o

(1979) , P i n t o et a 1 (1982) and P i n t o & N e i d e r t

(1982, 1983a) have l e d t o a b e t t e r u n d e r s t a n d i n g o f

t h e f a c t o r s involved. Use of d imens iona l a n a l y s i s

sugges ted t h a t t h e r a t e of a i r demand (q ) p e r u n i t a

width of channe l shou ld depend upon t h e f o l l o w i n g

p a r a m e t e r s :

where t h e f i r s t f o u r q u a n t i t i e s on t h e r igh t -hand s i d e

a r e t h e Froude, Reynolds , Weber and E u l e r numbers

r e s p e c t i v e l y ; dp is t h e p r e s s u r e d i f f e r e n c e between

t h e upper and lower s u r f a c e s of t h e j e t . The E u l e r

and Froude numbers i n f l u e n c e t h e l e n g t h and c u r v a t u r e

of t h e j e t , whi le t h e v a l u e of t h e Weber number

d e t e r m i n e s whether i t b r e a k s up i n t o a s p r a y and t h u s

e n t r a i n s a i r s t r o n g l y .

The air demand cannot be considered in isolation from

the head-loss characteristics of the air supply

system, which can be expressed in the general form

where Qa is the total rate of air flow, p is its a

density, A is the cross-sectional area of the duct a

and c is (normally) constant for a particular

arrangement. For a given flow velocity, the rate of

air entrainment on the underside of the jet depends

upon the length L of the cavity, which in turn is C

affected by the pressure difference 4: increasing &

decreases L and vice versa. The value of bp adjusts C

until the air demand of the jet matches the rate of

flow through the air duct. If air is supplied to the

cavity from lateral outlets in the side wall, there

will be a variation of 4, across the width of the

channel; the difference is largest at the outlet and

decreases towards the centre of the channel.

Pinto et a1 (1982) determined values of the parameter

q /VLc for the aerators at Foz do Areia Dam (Brazil): a the air demand ratio 6 = Qa/Q was obtained from

prototype measurements, the cavity length Lc from a

1:50 scale model and the depth of flow d by means of

calculations. Over a six-fold range of water

discharges it was found that the quantity q /VL was a c

approximately constant, i.e.

where k = 0.033 for air supplied laterally from both

sides of the channel (70.610 wide) and k = 0.023 with

air supplied from only one side. However, later model

tests which Pinto h Neidert (1983a) carried out over a

wider range of conditions showed that k was not in

f a c t a c o n s t a n t , bu t v a r i e d s i g n i f i c a n t l y w i t h F , Ee

and h / d . Values of F and h / d f o r a p a r t i c u l a r dam d o

n o t a l t e r g r e a t l y w i t h f low c o n d i t i o n s , b u t t h e

s i g n i f i c a n c e of t h e E u l e r number E shows t h a t t h e e

c h a r a c t e r i s t i c s of t h e a i r supp ly sys tem have a n

i m p o r t a n t e f f e c t on t h e amount of e n t r a i n m e n t . The

i n f l u e n c e of s u r f a c e t e n s i o n can be n e g l e c t e d i f t h e

v a l u e of t h e Weber number W > 1000 a p p r o x i m a t e l y ( s e e e

E q u a t i o n F.38).

Pan e t a 1 (1980) c a r r i e d o u t a l a b o r a t o r y s t u d y o f

ramp a e r a t o r s which l e n d s s u p p o r t t o t h e l a t e r work o f

P i n t o e t a 1 d e s c r i b e d above. V e r t i c a l and

l o n g i t u d i n a l measurements of a i r c o n c e n t r a t i o n were

made i n o r d e r t o d e t e r m i n e how t h e a i r was e n t r a i n e d

upwards i n t o t h e f low from t h e c a v i t y c r e a t e d by t h e

a e r a t o r . The l e n g t h L of t h e c a v i t y was t a k e n a s C

b e i n g t h e d i s t a n c e from t h e a e r a t o r t o t h e p o i n t on

t h e f l o o r of t h e c h a n n e l where t h e a i r c o n c e n t r a t i o n

d e c r e a s e d t o 60%. Based on t h e v e r t i c a l p r o f i l e of

a i r c o n c e n t r a t i o n a t t h e downstream end of t h e c a v i t y ,

t h e r a t e o f f low of e n t r a i n e d a i r was c a l c u l a t e d t o

be

where V is t h e f low v e l o c i t y a t t h e end o f t h e c a v i t y d

( n o t a t t h e a e r a t o r ) . T h i s r e s u l t a g r e e d w e l l w i t h

t h e model d a t a , and h a s a s i m i l a r form t o E q u a t i o n

F.40 which was de te rmined from p r o t o t y p e

measurements.

Pan 6 Shao (1984) a l s o c o n s i d e r e d a n a l t e r n a t i v e

approach t o p r e d i c t i n g t h e a i r demand t h a t would n o t

r e q u i r e p r i o r d e t e r m i n a t i o n of t h e c a v i t y l e n g t h .

A n a l y s i s of l a b o r a t o r y and p r o t o t y p e d a t a , i n t e rms of

t h e non-dimensional p a r a m e t e r X d e f i n e d i n E q u a t i o n U

F.37, l e d t o t h e f o l l o w i n g e m p i r i c a l e q u a t i o n f o r t h e

a i r demand produced by a ramp a n d / o r s l o t ( b u t no

o f f s e t ) i n a channe l of c o n s t a n t s l o p e .

f o r X > 1 U

(F.42)

T h i s r e s u l t may n o t be g e n e r a l l y a p p l i c a b l e because i t

d o e s n o t t a k e accoun t of the head- loss c h a r a c t e r i s t i c s

of t h e a i r supp ly system. On a channe l of v a r y i n g

s l o p e , t h e a i r demand i s a l t e r e d by t h e e f f e c t of

c e n t r i p e t a l p r e s s u r e .

Model t e s t s f o r f o u r a e r a t o r s t o be used on t h e

s p i l l w a y of La iban dam ( P h i l i p p i n e s ) were d e s c r i b e d by

Koschi tzky e t a1 (1984) . It was found t h a t , p rov ided

t h e a i r supp ly system d i d n o t l i m i t t h e amount of

e n t r a i n m e n t , t h e a i r demand r a t i o p f o r a g i v e n

a e r a t o r depended on ly upon t h e Froude number of t h e

f low ( r e g a r d l e s s of t h e a b s o l u t e v a l u e s of v e l o c i t y

and w a t e r d e p t h ) . The r e s u l t s a l s o showed t h a t t h e

p resence of a n a e r a t o r upst ream tended t o i n c r e a s e t h e

amount of a i r e n t r a i n e d a t an a e r a t o r downstream.

Usefu l p r o t o t y p e d a t a on t h e performance of f o u r

a e r a t o r s t e s t e d on c h u t e s 1 and 3 of Gur i dam

(Venezuela) a r e g iven by Marcano h C a s t i l l e j o (1984) .

The v a l u e s of t h e e n t r a i n m e n t parameter k i n Equat ion

F.40 were found t o be approx imate ly c o n s t a n t f o r each

a e r a t o r , and v a r i e d between k = 0.011 f o r a 0.10m h i g h

ramp p l u s 2.0m deep groove and o f f s e t , and k - 0.073

f o r a 0.75m h i g h ramp. It was found t h a t i t was

d i f f i c u l t t o p r e d i c t o r t o reproduce c o r r e c t l y i n a

model t h e under p r e s s u r e s t h a t occur red a t t h e

p r o t o t y p e a e r a t o r s . A s a r e s u l t , t h e models tended t o

o v e r - e s t i m a t e t h e l e n g t h s of t h e a i r c a v i t i e s .

Brusch in (1985) a n a l y s e d t h e Foz do Are ia d a t a

t o g e t h e r w i t h r e s u l t s from a model of P i e d r a d e l

Agui la Dam (Argen t ina ) . Using t h e o v e r a l l s t e p h e i g h t

W i n s t e a d of L a s t h e c h a r a c t e r i s t i c l e n g t h l e d t o C

t h e f o l l o w i n g formula f o r t h e air-demand r a t i o

T h i s r e s u l t does n o t t a k e accoun t of t h e u n d e r - s u r f a c e

p r e s s u r e , and i t s v a l i d i t y h a s been q u e s t i o n e d by

De F a z i o h Wei (1985).

Wood (1985) a l s o s t u d i e d t h e Foz do Are ia d a t a a n d

produced t h e f o l l o w i n g e q u a t i o n f o r d e t e r m i n i n g t h e

v a l u e of t h e f a c t o r k i n Equa t ion F.40.

where t h e v a l u e of t h e Froude number F a t t h e s t a r t k

of a i r e n t r a i n m e n t is g i v e n by

Model tests of a n a e r a t o r w i t h a n o f f s e t , b u t n o

d e f l e c t o r (h = 0 ) f o r Clyde Dam (New Zealand) gave

lower v a l u e s of k then p r e d i c t e d by Equa t ion F.44.

Low (1986) d e s c r i b e s model t e s t s on a e r a t o r s f o r t h e

s p i l l w a y of Clyde Dam (New Zealand) c a r r i e d o u t a t a

s c a l e of 1 :15. R e s u l t s a r e g iven f o r a e r a t o r s of t h e

t y p e shown i n F i g u r e a c ( b u t w i t h o u t t h e rounded

c o r n e r ) f o r ramp a n g l e s of 0 = 4' and 5.7' and a

s p i l l w a y s l o p e of 1:O.E. The measured a i r demands

were approximated by a n e q u a t i o n of t h e form:

where t h e f i r s t term on t h e r ight-hand s i d e d e s c r i b e s

t h e e f f e c t of f low v e l o c i t y and t h e second term t h e

e f f e c t of t h e sub-atmospher ic p r e s s u r e i n t h e a i r

c a v i t y . The f a c t o r s a l , a 2 , a 3 and a, ,depended on t h e

geometry of t h e a e r a t o r . Use of a d e n t a t e d ramp

upst ream of t h e s l o t reduced t h e tendency f o r p t o

d e c r e a s e a s t h e p r e s s u r e d i f f e r e n c e 4 was i n c r e a s e d

( i . e . i t had t h e e f f e c t of r educ ing t h e v a l u e of a 3 i n

E q u a t i o n F.46). S i n c e t h e tests were c a r r i e d o u t on a

s e c t i o n a l model, i t was no t p o s s i b l e t o d e t e r m i n e

d i r e c t l y t h e t o t a l a i r demand f o r a n a e r a t o r spanning

t h e f u l l wid th of t h e s p i l l w a y . The problem i s

complex because t h e p r e s s u r e d i f f e r e n c e 4 i n t h e a i r

c a v i t y v a r i e s w i t h t r a n s v e r s e d i s t a n c e from t h e d u c t s

i n t h e s i d e w a l l s of t h e s p i l l w a y . Low d e s c r i b e s a

t h e o r e t i c a l model of t h e a i r supp ly sys tem which

e n a b l e s t h e t o t a l a i r demand t o be c a l c u l a t e d u s i n g

t h e d a t a from t h e s e c t i o n a l model. Measurements were

a l s o made of t h e v e r t i c a l d i s t r i b u t i o n of a i r i n t h e

f low downstream of t h e a e r a t o r s . These showed t h a t

t h e a i r c o n c e n t r a t i o n c l o s e t o t h e bed d e c r e a s e d

f a i r l y r a p i d l y downstream of t h e rea t t achment p o i n t of

t h e f low. I n model t e r m s , t h e c o n c e n t r a t i o n a t a

h e i g h t of l O m m above t h e bed dec reased t o C = 10%

w i t h i n a d i s t a n c e t h a t v a r i e d from abou t 0.1-1.0m f o r

Froude numbers between F = 7.0 and 13.4 .

B r e t s c h n e i d e r (1986) t e s t e d models of s l o t - t y p e

a e r a t o r s t o d e t e r m i n e t h e c r i t i c a l f low v e l o c i t y V k

f o r t h e s t a r t of a i r e n t r a i n m e n t . The b e s t - f i t

c o r r e l a t i o n o b t a i n e d f o r f i v e s i z e s of s q u a r e s l o t

was :

where t h e b r a c k e t e d term on t h e l e f t -hand s i d e i s a

t y p e of Reynolds number and t h a t on t h e r ight-hand

side a type of Weber number. However, the form of the

correlation was not fully tested because the fluid

properties ( p , v, d) were not varied. For water at

20°C, Equation F.47 becomes

where V i s in m/s and d in m. If gravity is assumed k

to be implicit in the factor 18.2, then this result is

equivalent to a critical Froude number for air

entrainment of F = 5.8. k

Bruschin (1987) proposed an alternative type of

entrainment function to that given by Equation F.40.

The characteristic length is postulated to be a

certain vertical "roughness" index 6 rather than the

cavity length L . The proposed equation has the C

form:

Use of some prototype data, together with an assumed

threshold velocity of V = lm/s, gave values of 6 = k 0.2-0.4m. The factors which may influence 6 were not

discussed.

Pinto (1986) used photographs of flow conditions in

the Foz do Areia spillway to estimate the amount of

bulking and hence the total amount of air entrainment.

At the downstream end of the spillway the mean air

concentration was calculated to vary between about 39%

and 47% for unit water discharges ranging from

20.8 to 120m 3/s/m. The longitudinal flow profiles

showed that most oE the air entrainment occurred over

a distance of about 20-30m downstream of each of the

three aerators. However, the aerators themselves

supplied only a relatively small proportion of the

total air in the Elow (of the order of 25% or less).

Most of the air appeared to be entrained at the

surface as a result of the very strong flow turbulence

generated by the aerators; this entrainment was

distinct from the normal self-aeration considered in

Section F.2. These findings suggest that factors not

highlighted by model tests may contribute to the

effectiveness of aerators in preventing cavitation

damage.

A recognised problem with reduced-scale models of

aerators is that they may significantly underestimate

the air demand in the prototype. This topic is

considered in detail in Section G.2.

The required spacing between successive aerators is

determined by the rate at which the local air

concentration near the floor of the channel decreases

with distance. Data for Bratsk Dam (USSR) given by

Kudriashov et a1 (1983) showed that the mean air

concentration decreased at a rate of 0.4% per metre of

channel, but the loss rate is believed to vary with

the slope and flow velocity (Bratsk spillway has a

steeper-than-usual slope of 51').

Prusza et a1 (1983) summarise Russian information on

aeration and give the following loss rates for

different types of channel

Straight section 0.15 - 0.20% per metre Concave section (bucket) 0.50 - 0.60% per metre Convex section 0.15 - 0.20% per metre

Model data for San Roque Dam presented by Volkart &

Chervet (1983) showed that the local air concentration

near the bed decreased from about 50% to less than 10%

in a distance of about 15m, for flow velocities in the

range of 25 - 32m/s (in prototype terms). However,

the loss rate is likely to be subject to significant

s c a l e e f f e c t s . It was found t h a t t h e r e q u i r e d s p a c i n g

between a e r a t o r s depended on t h e f low v e l o c i t y i n t h e

s p i l l w a y and n o t on t h e d i s c h a r g e of wa te r p e r u n i t

width .

V o l k a r t & Rutschmann (1984a) q u o t e Semenkov h L e n t j a e v

(1973) a s g i v i n g t h e l o s s r a t e f o r a s t r a i g h t channe l

a s 0.5 - 0.8% per me t re and f o r a channe l w i t h concave

c u r v a t u r e 1 .2 - 1.5% p e r metre . D i s t a n c e s between

a e r a t o r s a r e t y p i c a l l y i n t h e range 30-100m.

Hamilton (1984) sugges ted t h a t t h e l o s s r a t e might be

expec ted t o be p r o p o r t i o n a l t o t h e l o c a l a i r

c o n c e n t r a t i o n , i . e .

l e a d i n g t o a n e q u a t i o n of t h e f o r m

Data on t h e d e c r e a s e of a i r c o n c e n t r a t i o n n e a r t h e

f l o o r of B r a t s k Dam (C = 85% t o 35% i n 53m) g i v e s a

v a l u e of j = 0.017 p e r me t re .

Cui (1985) measured bo th t h e v e r t i c a l and l o n g i t u d i n a l

v a r i a t i o n of a i r c o n c e n t r a t i o n downstream of a e r a t o r s .

An e x p o n e n t i a l type of e q u a t i o n was f i t t e d t o t h e d a t a

on t h e l o n g i t u d i n a l d e c r e a s e of c o n c e n t r a t i o n , b u t t h e

form of t h e e q u a t i o n s u g g e s t s t h a t i t may be s p e c i f i c

t o t h e p a r t i c u l a r s t u d y .

When d e s i g n i n g a n a e r a t i o n sys tem i t i s n e c e s s a r y t o

choose a f i g u r e f o r t h e maximum a i r v e l o c i t y i n t h e

d u c t s i n o r d e r t o avo id c o m p r e s s i b i l i t y problems and

objectionable noise. Limiting velocities recommended

or used by various authors are as follows:

Ref erence Maximum Air Velocity

(m/s)

Falvey (1980) 30 (continuous operation)

Haindl (1984) 4 0 Billore et a1 (1979) 50 Coleman et a1 (1983) 5 0 Eccher S Siegenthaler (1982) 60 Falvey (1980) 90 (short

duration) Prusza et a1 (1983) 100 - 120

Design pressures at aerators supplied by air ducts are

typically in the range & = 0.5m to 2.0m head of water

below atmospheric pressure. Where side-wall

deflectors are used to supply air to aerators, the

pressure differences are normally smaller ( c 0.5m head

of water).

Aerators are reported to have been successful in

preventing cavitation damage at the following dams:

Bratsk, Calacuccia, Emborcaqao (V 6 35m/s), Foz do

Areia (V 6 43m/s), Grand Coulee, Guri

(Qw 6 10 000m3/s), Heart Butte. Mica, Nurek, Tarbela

(tunnel no 3) and Yellowtail.

F.4 Aeration in The high speed flow of water downstream of gates in h

tunnels tunnels leads to air entrainment at the free surface

and also a flow of air in the space above it, the

velocity of which may sometimes be greater than that

of the water itself. What may be termed this

"natural" air demand is usually met by means of a

system of galleries or ducts connecting to the gate

shaft. Aerators may also be used to prevent

cavitation damage to the floor and walls of the

tunnel. The devices operate in a similar way to those

on spillways; side deflectors are often provided in

the walls to allow air to flow from the surface to the

invert of the tunnel. The additional "forced" air

demand can thus be supplied by means of the gate shaft

and its connecting ducts.

The natural air demand created by the high velocity

flow in a closed conduit will be considered first.

Falvey (1980) gives a useful guide to the subject and

describes the various types of air-water flow that can

occur. It is important to distinguish cases where a

tunnel downstream of a gate flows part-full over its

full length from those where the tunnel is sealed by a

hydraulic jump; in the latter cases the air flow is

determined by the amount of entrainment in the jump

and by the capacity of the flow to transport the

bubbles of air along the tunnel.

Kalinske h Robertson (1943) used model data for the

air demand in tunnels with hydraulic jumps to obtain

the formula

Qa p = - = 0.0066 (F - l) 1.4 9,

, for 1.5 6 F < 30 (F.52)

where the Froude number just upstream of the jump is

given by

Falvey (1980) demonstrates satisfactory agreement

between Equation F.52 and measurements from three

prototype tunnels for values of 2.5 < F 1 6 50.

Campbell h Guyton (1953) compared Kalinske h

Robertson's formula with data from five different

dams, and found that it under-predicted the air

demand. The maximum rates of air flow (Q ) occurred a

at gate openings of about 80%, and the upper limit to

the field data for tunnels with jumps was given by

p = 0.04 (Fc - 1)0'85 , for 3.5 S F < 10 C

(F .54)

where F is the value of the Froude number at the vena C

contracta.

The US Army Corps of Engineers (1964) reviewed model

and prototype information on air demand, and

recommended the following equation for flows with

hydraulic jumps

Uppal et a1 (1965) carried out tests on a 1:17 scale

model of a 2.59111 diameter tunnel of horseshoe

cross-section downstream of a control gate. The

tunnel flowed part-full for gate openings less than

90%, and measured air demands were greater than

predicted by Equations F.52 and F.54. The maximum

value of B occurred at a 40% gate opening and the maximum air flow Q at a 60% opening.

a

Levin (1965) analysed information from previous

studies of air demand in tunnels with jumps, and

proposed the formula

where H is the total head upstream of the gate and d C

is the depth of flow at the vena contracta downstream 1

of the gate; for H/d >> 1, the quantity (2H/dc)qs C

approximately equal to F . For a circular tunnel with C

carefully designed gate slots, G = 0.025 - 0.040. Where there is a gradual transition from a rectangular

t o a c i r c u l a r c r o s s - s e c t i o n downstream of a g a t e , t h e n

G = 0.040 - 0.060. I f t h e t r a n s i t i o n i s l e s s g r a d u a l

and flow s e p a r a t i o n o c c u r s , G = 0.08 - 0.12. The r a t e

of f low i n t h e a i r supp ly sys tem is g i v e n by

where

and ET i s t h e sum of t h e v e l o c i t y head c o e f f i c i e n t s

f o r form l o s s e s i n t h e d u c t , A i s t h e Darcy-Weisbach

f r i c t i o n f a c t o r , L i s t h e l e n g t h of t h e d u c t , and Aa a

and Ra a r e r e s p e c t i v e l y i t s c r o s s - s e c t i o n a l a r e a and

h y d r a u l i c r a d i u s .

F i e l d d a t a f o r t u n n e l s f lowing p a r t f u l l , w i thou t a

jump, were o b t a i n e d by Wisner (1965) who f i t t e d t h e

f o l l o w i n g e q u a t i o n t o t h e measurements of a i r demand

p = 0.024 (Fc - , f o r 3 < F F 20 C

(F .59)

A t s m a l l g a t e openings t h e s l o t s g i v e r i s e t o a

s p r a y - t y p e f low which e n t r a i n s a i r more s t r o n g l y , and

f o r t h i s c o n d i t i o n t h e a i r demand i s g i v e n by

p = 0.033 (Fc - , f o r 20 < Fc '< 60 (F .60)

Lysne h Guttormsen (1971) measured t h e a i r demand i n

high-head t u n n e l s i n two Norwegian dams. Spray

f o r m a t i o n a t g a t e open ings of 5-10% produced t h e

l a r g e s t v a l u e s of p, b u t t h e r a t e s of a i r f low

i n c r e a s e d s t e a d i l y a s t h e g a t e s were opened. The

upper bound t o t h e d a t a was d e s c r i b e d by t h e e q u a t i o n

where S i s t h e a r e a of opening of t h e g a t e and A i s

t h e c r o s s - s e c t i o n a l a r e a of t h e t u n n e l . P r e s s u r e s

downstream of t h e g a t e s were 80-90% of a t m o s p h e r i c

p r e s s u r e , and t h i s r e d u c t i o n needs t o be t aken i n t o

accoun t when c a l c u l a t i n g v a l u e s of t h e c a v i t a t i o n

pa ramete r K ( see E q u a t i o n ( 2 ) ).

Sharma (1976) s t u d i e d a i r e n t r a i n m e n t i n a r e c t a n g u l a r

c o n d u i t O.Lm X 0.15m and a l s o made use of some

p r o t o t y p e d a t a . For f low w i t h a h y d r a u l i c jump, i t

was found t h a t Ka l inske & R o b e r t s o n ' s E q u a t i o n F.52

gave r e a s o n a b l e r e s u l t s i f t h e v a l u e of t h e Froude

number was c a l c u l a t e d a t t h e vena c o n t r a c t a (Fc)

i n s t e a d of j u s t ups t ream of t h e jump (F1) . T h i s

a v o i d s t h e problem of having t o e s t i m a t e s e p a r a t e l y

t h e a i r e n t r a i n m e n t a l o n g t h e f r e e s u r f a c e a s w e l l a s

a t t h e jump i t s e l f . Sharma a l s o s t u d i e d t h e c a s e of

p a r t - f u l l f low wi thou t a jump and o b t a i n e d t h e

r e l a t i o n

p = 0.09 F f o r 5 4 F < 60 C ' C

(F.62)

For sp ray- type f l o w a t s m a l l g a t e open ings , t h e a i r

demand was g iven by

p = 0.2 Fc , f o r 20 \< Fc \< 100 (F.63)

Rabben e t a 1 (1983) , Rabben (1984) and Rabben & Rouv6

(1984) g i v e r e s u l t s of model t e s t s t o de te rmine t h e

a i r demand downstream of a g a t e i n a r e c t a n g u l a r

t u n n e l . The a i r demands were found t o depend on t h e

s i z e and h e a d l o s s c h a r a c t e r i s t i c s of t h e a i r d u c t s , a s

d e s c r i b e d by a n e f f e c t i v e a r e a

where A i s t h e c r o s s - s e c t i o n a l a r e a of t h e d u c t and a

X< is t h e sum of t h e v a r i o u s head- loss c o e f f i c i e n t s .

T e s t s were c a r r i e d o u t on t h r e e g e o m e t r i c a l l y s i m i l a r

models, t h e l a r g e s t having t u n n e l s of h e i g h t 0.25m and

0.32111 upst ream and downstream of t h e v e r t i c a l g a t e .

For t h e c a s e of f low with a h y d r a u l i c jump, t h e a i r

demand i n t h e l a r g e s t model was g iven by:

where A is t h e t o t a l downstream a r e a of t h e t u n n e l . t

For f r e e f low downstream of t h e g a t e , t h e

cor responding r e s u l t was:

The r e s u l t s were compared wi th d a t a from t h e two

s m a l l e r models, which r e l a t i v e t o t h e l a r g e s t one had

s c a l e r a t i o s of 1:1.333 and 1:2.0. For t h e c a s e of

f l o w w i t h a h y d r a u l i c jump, i t was found t h a t t h e

Froude c r i t e r i o n c o r r e c t l y s c a l e d t h e a i r demands;

Equa t ion F.65 may t h e r e f o r e be v a l i d o u t s i d e t h e

e x p e r i m e n t a l range. On t h e o t h e r hand, t h e r e s u l t s

f o r t h e c a s e of f r e e flow showed t h a t t h e a i r demands

d i d n o t s c a l e a c c o r d i n g t o t h e Froude c r i t e r i o n ;

Equa t ion F.66 s h o u l d n o t t h e r e f o r e be used d i r e c t l y ,

a l t h o u g h Rabben C Rouv6 (1984) do g i v e a method f o r

e s t i m a t i n g t h e a p p r o p r i a t e s c a l e f a c t o r . T e s t s were

a l s o c a r r i e d o u t on a n a e r a t o r c o n s i s t i n g of a n o f f s e t

i n t h e f l o o r of t h e t u n n e l downstream of t h e g a t e ; a s

i n t h e c a s e of f r e e f low, i t was found t h a t t h e a i r

demands were s u b j e c t t o s c a l e e f f e c t s . These

d i s c r e p a n c i e s were b e l i e v e d t o occur because t h e

Froud ian s c a l i n g d i d n o t reproduce c o r r e c t l y t h e

f o r m a t i o n of s p r a y .

Ouazar h Lejeune (1984) analysed prototype data on air

entrainment in tunnels with jumps, and obtained the

relation

Model tests were also carried out in a gated conduit

measuring lOOmm X 150mm in section, and equipped with

a vacuum system to reproduce the pressure reductions

correctly. Measurements of air demands for flows with

jumps in this and other models were fitted by the

equation

Comparison with Equation F.67 shows that the amount of

air entrainment in models tends to be proportionately

lower than in prototype tunnels. Tests were also made

with the model tunnel flowing freely, and it was found

that the air demand ratio p depended upon the flow

velocity and not the Froude number. This indicates

that Froudian scaling may not be appropriate for

modelling air entrainment in tunnels flowing freely.

Haindl (1984) carried out experiments on the

entrainment of air by a jump in a rectangular conduit

measuring 0.266m X 0.200m. Some of the tests gave

higher values of p than Equation F.52, and inclusion

of Campbell h Guyton's field data led to the following

formula for the maximum air-water ratio

1.4 p = 0.015 (F - l) , for 3 & F I 6 5 0 (F.69)

Laboratory experiments to determine the amounts of air

entrained by hydraulic jumps in a closed conduit were

carried out by Ahmed et a1 (1984). The cross-section

of the conduit measured 0.1410 X 0.14~1, and tests were

done at slopes of 90°, 6 0 ° , 45', 30' and 10".

Measurements were made of the total rate of air

entrainment at the toe of the jump and the net rate at

which it was transported downstream by the flow.

Analysis of the data from many tests led to the

following equation for the net air demand:

"k p = 0.00234 [l + 4.87 exp [-0.35(~~-1) ) ] [ I - ~ ] ~

Here V is the velocity of the jet entering the jump,

E l is the corresponding Froude number (see Equation

F.53), and Vk is the flow velocity at which air

entrainment starts; note that the slope of the

conduit was not found to be significant. The equation

was developed assuming a fixed value of V = 0.8m/s. k

The last bracketed term on the right-hand side of the

equation may help to explain why air demands in models

can be subject to scale effects. At high flow

velocities, such as occur in prototype tunnels, this

term tends towards unity; in Froudian models the

velocities are lower, and the last term may become

significantly less than unity. Comparison of this

laboratory equation with prototype data would help to

establish its general validity. It should be noted

that the result is based on conditions just upstream

of the jump, whereas most of the others described in

this section relate to conditions at the vena

contracta formed just downstream of a gate.

The "natural" air demands predicted by some of the

equations described above are compared in Figure 10,

and it can be seen that there are quite substantial

differences between some of them. Overall, it appears

that, for a given Froude number, the value of p is

greater if the tunnel flows part full than if it is

s e a l e d by a jump. Spray f low produces t h e h i g h e s t

v a l u e s of p, b u t s i n c e i t o c c u r s a t smal l g a t e

open ings i t w i l l n o t normal ly g i v e r i s e t o t h e maximum

r a t e of a i r f low, . The p resence of a i r i n t u n n e l s Q a

f l o w i n g f u l l c a n cause u n d e s i r a b l e p r e s s u r e shocks ,

and i t may need t o be removed by means of d e a e r a t i o n

chambers.

D e t a i l s of a e r a t o r s i n v a r i o u s p r o t o t y p e t u n n e l s

( b u i l t o r p lanned) a r e g iven i n Tab le 3. An a e r a t o r

was added t o t h e 9.76m d iamete r t u n n e l of Y e l l o w t a i l

Dam t o p r e v e n t c a v i t a t i o n damage t h a t had been found

t o o c c u r a t t h e s t a r t of a v e r t i c a l bend. Model

s t u d i e s c a r r i e d o u t by Colega te (1971) showed t h a t t h e

shape of t h e a e r a t o r r e q u i r e d c a r e f u l d e s i g n . A s l o t

around t h e p e r i m e t e r of t h e c o n d u i t f i l l e d too e a s i l y

w i t h wa te r and thus d i d n o t a e r a t e e f f i c i e n t l y ;

na r rowing t h e top of t h e s l o t made t h e problem worse.

A d e f l e c t o r was t h e r e f o r e added upst ream of t h e s l o t ,

and was s u c c e s s f u l i n keeping i t c l e a r of w a t e r a t a l l

d i s c h a r g e s . However, t h e d e f l e c t o r produced f i n s of

w a t e r downstream, and i t was n e c e s s a r y t o e n s u r e t h a t

t h e s e were n o t l a r g e enough t o s e a l t h e p ipe . It had

been i n t e n d e d t o add two o t h e r a e r a t o r s , one nea r t h e

head of t h e t u n n e l and t h e o t h e r a t t h e downstream end

of t h e v e r t i c a l bend. However, t h e model t e s t s showed

t h a t they would n o t o p e r a t e s a t i s f a c t o r i l y , and t h e y

were t h e r e f o r e no t adop ted .

Based on USBR e x p e r i e n c e on seven t u n n e l s p i l l w a y s ,

Wagner 6 J a b a r a (1971) recommended t h e u s e of o f f s e t s

a s a e r a t o r s . On t h e f l o o r of t h e c h a n n e l , t h e amount

of o f f s e t shou ld be 116 of t h e g a t e wid th , whi le a t

t h e s i d e w a l l s i t shou ld be 1 /12 of t h e g a t e width .

I f l a r g e r o f f s e t s a r e used, f i n s of water may s e a l t h e

t u n n e l o r o v e r t o p t h e s i d e w a l l s .

Beich ley h King (1975) d e s c r i b e a e r a t o r s used i n t h r e e

US high-head t u n n e l s and make t h e f o l l o w i n g

recommendations:

1. For new d e s i g n s , w a l l and f l o o r o f f s e t s a r e

normal ly b e t t e r than a i r s l o t s and

d e f l e c t o r s . The l a t t e r may be t h e o n l y

s o l u t i o n f o r e x i s t i n g s t r u c t u r e s ;

2. O f f s e t s should be a minimum of lOOmm (116 of

g a t e frame width a t f l o o r , 1 / 1 2 a t s i d e

w a l l s ) . A i r s l o t s a r e n o t r e q u i r e d w i t h

o f f s e t s ;

3. Wall d e f l e c t o r s need t o be used i n

c o n j u n c t i o n w i t h a i r s l o t s i f t h e downstream

s i d e s of t h e t u n n e l a r e p a r a l l e l . The w a l l

d e f l e c t o r s shou ld n o t p r o j e c t more t h a n 25mm

i n t o t h e f low w i t h a s l o p e of 1:30;

4. F l o o r d e f l e c t o r s s h o u l d s t a r t a t t h e end of

t h e g a t e f rame, have a r i s e of a t l e a s t

50mm, and a s l o p e n o t exceed ing 1:9 (6 .3 ' ) ;

5. Air s l o t s s h o u l d be s q u a r e i n c r o s s - s e c t i o n .

A s i z e of 300mm X 300mm s h o u l d be a d e q u a t e

f o r g a t e s measuring up t o 1.2m X 2.3m w i t h

heads of up t o 100m;

6. The downstream edge of an a i r s l o t shou ld b e

o f f s e t 25-5Dmm away from t h e f low, and any

t r a n s i t i o n shou ld be made w i t h s l o p e s n o t

g r e a t e r t h a n 1 :20 ( f o r V < 12m/s), 1:50 ( V <

27m/s) and 1:100 ( V < 371111s).

Rabben e t a 1 (1983) s t u d i e d a i r en t ra inment i n a model

of a t u n n e l w i t h a f l o o r o f f s e t l o c a t e d downstream of

a g a t e . The a i r demand was found t o be l i n e a r l y

r e l a t e d t o t h e l e n g t h L of t h e c a v i t y formed by t h e C

o f f s e t

where d is t h e d e p t h of f low a t t h e vena c o n t r a c t a . C

The e q u a t i o n i s v a l i d f o r v a l u e s of Lc/dc C 20 and

4 < F ,< 18; f o r Lc/dc > 20 t h e j e t b r e a k s up and t h e C

a i r c a v i t y i s no l o n g e r s e a l e d .

H a r t (1982) and McGee (1984) d e s c r i b e p r o t o t y p e

measurements a t Libby Dam (USA) of a i r demand i n t h r e e

s l u i c e s , each measur ing 3m X 6.7m h i g h and c o n t r o l l e d

by a t a i n t e r g a t e . C a v i t a t i o n damage had o c c u r r e d

p r e v i o u s l y , s o an a e r a t o r , c o n s i s t i n g of a d e f l e c t o r

and a i r s l o t ( s e e Tab le 3 ) . was f i t t e d immediate ly

downstream of each g a t e . The t o t a l a i r demands

( n a t u r a l p l u s f o r c e d ) f o r p a r t - f u l l f low w i t h o u t a

jump were found t o be i n r e a s o n a b l e agreement w i t h

Sharma 's Equa t ions F.62 and F.63, which do n o t t a k e

accoun t of t h e e f f e c t of a n a e r a t o r . The lowes t

p r e s s u r e i n t h e a e r a t o r s was abou t -1.3m head of

w a t e r , and t h e maximum v a l u e of p was approx imate ly

3.3 ( i . e . C = 77%).

Measurements of p r o t o t y p e a i r demands a t Krasnoyarsk

and Ze ia Dams (USSR) a r e d e s c r i b e d by Abelev e t a 1

(1983) . The d e s i g n of t h e temporary o u t l e t t u n n e l f o r

e a c h dam was s i m i l a r , and i n c l u d e d a s t e p a e r a t o r

downstream of t h e t a i n t e r g a t e , w i t h a i r p rov ided by

d u c t s from t h e g a t e s h a f t . I n t h e c a s e of t h e e a r l i e r

Krasnoyarsk Dam, t h e a i r supp ly sys tem was n o t

adequa te ; a i r v e l o c i t i e s i n t h e d u c t s r eached 130 m / s ,

and c a v i t a t i o n o c c u r r e d downstream of t h e a e r a t o r .

The t u n n e l s f lowed p a r t - f u l l downstream of t h e g a t e s ,

and t h e a i r demands ( n a t u r a l p l u s f o r c e d ) were h i g h e r

t h a n p r e d i c t e d by Wisner ' s E q u a t i o n F.59. The d a t a

f o r t h e two dams were f i t t e d by t h e formula

p = 0.11 (F-l), for 2.5 6 F 6 16 (F.72)

where F is calculated using the area and depth of

opening of the gate.

Vernet h Larrea (1985) give model and prototype

measurements of air entrainment for an aerator used at

Alicura Dam (Argentina). The aerator consists of a

deflector and air slot, and is positioned 50m

downstream of a gate at the point where the steel

lining to the 6.55m X 3.7m high channel ends (the

channel is formed in a gm diameter tunnel). The

tunnel flows part-full, and the air demand (natural

plus forced) was in reasonable agreement with Sharma's

Equation F.62 and greater than predicted by Wisner's

Equation F.59. However, for the case of spray flow,

the measured value was close to Wisner's Equation F.60

and lower than given by Sharma's Equation F.63. It

should be remembered that these formulae relate to the

entrainment which occurs at the surface of the flow,

and do not allow for the additional demand created by

an aerator.

Montero et a1 (1986) describe the design of three

aerators used in the bottom outlet of Colbun Dam

(Chile). The outlet has a capacity of 730m3/s with

flow velocities of up to 45m/s. Control gates in twin

lined tunnels discharge into a rectangular channel

formed inside a larger diversion tunnel, which is of

oval cross-section. Tests were carried out on a 1:30

model of the complete outlet and a 1:18 model of the

gate section. A stepped aerator with wall slots was

located 4m downstream of the gates. A second aerator

with a combined floor ramp and step was placed 117m

downstream of the gates, at the point where the flow

discharged from the rectangular channel into the

original diversion tunnel. The third aerator was

located a further 117m downstream. and consisted of a

f l o o r ramp and s i d e s l o t s formed i n t h e w a l l s of t h e

d i v e r s i o n t u n n e l . The e f f e c t i v e n e s s of t h e a e r a t o r s

was demonstra ted by t h e f a c t t h a t i r r e g u l a r i t i e s i n

t h e d i v e r s i o n t u n n e l and f a i l u r e of a n epoxy m o r t a r

r e p a i r i n t h e r e c t a n g u l a r channe l d i d no t cause any

c a v i t a t i o n damage a f t e r 324 days of o p e r a t i o n a t f l o w s

of up t o 688m3/s.

F a c t o r s a f f e c t i n g t h e performance of t y p e s of a e r a t o r

used downstream of r a d i a l g a t e s were i n v e s t i g a t e d by

Pan 6 Shao (1986). The a e r a t o r s c o n s i s t e d of f l o o r

o f f s e t s ( w i t h and w i t h o u t ramps), and w a l l o f f s e t s

which were curved i n e l e v a t i o n t o accommodate t h e

ups t ream p r o f i l e of t h e g a t e . The geomet r i c f a c t o r s

which were v a r i e d i n t h e t e s t s were t h e s i z e of t h e

o f f s e t s , t h e a n g l e of t h e ramps and t h e s l o p e of t h e

r e c t a n g u l a r channe l downstream of t h e a e r a t o r .

Complicated semi-empir ica l fo rmulae were developed t o

p r e d i c t t h e c r i t i c a l Froude number f o r t h e s t a r t of

a e r a t i o n , and t h e l e n g t h s of t h e a i r c a v i t i e s produced

a t t h e f l o o r and t h e s i d e w a l l s . Formulae, based o n

E q u a t i o n F.41 and u s i n g t h e s e c a v i t y l e n g t h s , were

a l s o g i v e n f o r e s t i m a t i n g t h e o v e r a l l a i r demand of

t h e a e r a t o r .

I f a n a e r a t o r does n o t f u n c t i o n a s i n t e n d e d , o r i f t h e

f l o w c o n d i t i o n s a r e o u t s i d e i t s c o r r e c t o p e r a t i n g

r a n g e , i t may f i l l w i t h wa te r and n o t e n t r a i n a i r .

S t e p s and l a t e r a l o f f s e t s may t h e n a c t a s l a r g e s c a l e

i r r e g u l a r i t i e s c a u s i n g c a v i t a t i o n . Zhu (1984) t e s t e d

a model of a t u n n e l w i t h a s t e p p e d a e r a t o r downstream

of a r a d i a l g a t e . It was found t h a t t h e upst ream head

a t which c a v i t a t i o n would beg in a t t h e s t e p was

c o n s i d e r a b l y a f f e c t e d by t h e s l o p e of t h e t u n n e l

downstream of t h e s t e p : d e c r e a s i n g t h e s l o p e

i n c r e a s e d t h e v a l u e of t h e s a f e o p e r a t i n g head.

APPENDIX G

MODELLING AND INSTRUMENTATION

G.l C a v i t a t i o n Many a s p e c t s of mode l l ing c a v i t a t i o n have been d e a l t

w i t h i n S e c t i o n 2 and Appendices B t o F, and d e t a i l e d

d e s c r i p t i o n s of s t u d i e s a l r e a d y mentioned w i l l no t be

r e p e a t e d h e r e . S t u d i e s of c a v i t a t i o n can be c a r r i e d

o u t , a t a reduced s c a l e i n t h r e e main ways.

The f i r s t type of model i s o p e r a t e d a t a t m o s p h e r i c

p r e s s u r e a c c o r d i n g t o t h e s p e c i f i e d s c a l i n g law

( u s u a l l y Froud ian) . Measurements a r e made t o

d e t e r m i n e t h e p o i n t s of minimum p r e s s u r e a l o n g t h e

b o u n d a r i e s of t h e f low. Assuming t h e model and

p r o t o t y p e t o have e q u a l v a l u e s of t h e p r e s s u r e

c o e f f i c i e n t C (Equa t ion B . l ) , i t i s p o s s i b l e t o P

p r e d i c t whether p r e s s u r e s i n t h e p r o t o t y p e w i l l f a l l

t o t h e vapour p r e s s u r e of t h e wa te r and t h u s g i v e r i s e

t o c a v i t a t i o n . T h i s method c a n be used t o d e t e r m i n e

t h e l i m i t of i n c i p i e n t c a v i t a t i o n ( s e e 2.2) p rov ided :

1. t h e f low remains a t t a c h e d t o t h e b o u n d a r i e s

and t h e i n s t r u m e n t s a r e l o c a t e d a t t h e

p o i n t s of minimum p r e s s u r e ;

2. measurements a r e made of bo th f l u c t u a t i n g

and mean p r e s s u r e s ;

3. t h e d e g r e e of t u r b u l e n c e and t h e boundary

l a y e r development a r e s i m i l a r i n model and

p r o t o t y p e .

I f t h e f low s e p a r a t e s from a boundary, t h e l o w e s t

p r e s s u r e w i l l t e n d t o occur i n t h e body of t h e f l u i d ,

and t h e method w i l l t h e r e f o r e under -es t ima te t h e

l i k e l i h o o d of c a v i t a t i o n . R e s u l t s which p r e d i c t

p r e s s u r e s below the vapour p r e s s u r e of t h e l i q u i d a r e

therefore not reliable, although they do of course

indicate a serious danger of cavitation. In such

tests it is necessary to ensure that the response time

of the instrumentation is short enough to measure the

fluctuating pressures accurately. Information is

limited on levels of turbulence in prototype flows,

and it may be difficult to reproduce these correctly

in a model. Despite these potential problems, tests

at atmospheric pressure can be useful in comparing the

relative performances of different designs.

The second kind of test is carried out in a cavitation

tunnel, in which the pressure in the working section

is reduced below atmospheric so as to obtain equal

values in model and prototype of the parameter K

defined in Equation 2. Since the working section

flows full, this method is suitable for studying only

those situations in which free-surface effects are not

important, e.g. gate slots in tunnels and small

irregularities in spillway channels. With this

approach it is possible to detect incipient cavitation

directly, investigate the changes in flow which occur

as the cavitation becomes more intense, and measure

the amount of damage caused. However, all three of

these aspects are subject to scale effects which are

not well understood, particularly when the results are

to be applied to large hydraulic structures.

The third way of studying cavitation is to use a

vacuum test rig in which the air pressure can be

reduced below atmospheric. This allows models with

free-surface flows to be operated at prototype values

of K. Such facilities are appropriate for models of

spillways and stilling basins in which free-surface

effects have a significant influence on the behaviour

of the flow. However, vacuum test rigs can be

difficult and expensive to construct.

The inception and development of cavitation are

affected by the size and number of gas and dust nuclei

in the water. Keller (1972) demonstrated the

importance of nucleus size on conditions for incipient

cavitation about a streamlined body. Fresh tap water

gave K = 0.36, whereas similar water which had been i

filtered and left to stand for one hour gave Ki =

0.036. Although the overall gas contents oE the two

samples were nearly equal, measurements made using a

focused laser beam showed that the fresh tap water

contained many more large nuclei (with radii of the

order of 8pn or greater). Keller (1984) demonstrated

that repeatable results with water samples of

different quality could be obtained if K were i

calculated using p the critical pressure for cavity C '

growth (see Section 2.2), instead oE the vapour

pressure, . The value of p for each water sample Pv C

was found by producing a vortex within a specially

designed nozzle, and determining the pressure at which

cavitation started in the core of the vortex. This

type oE technique offers the prospect of more

consistent laboratory results. However, in order to

apply the results reliably, it will be necessary also

to obtain inEormation on the cavitational properties

of water under prototype conditions.

The limits of cavitation are themselves influenced by

the way in which they are measured (e.g. visually,

acoustically, by changes in turbulence levels, or by

the rate of pitting on a sample of soft material).

Tests can compare the relative resistances of

different materials, but it is difficult to predict

the amount of damage which might occur in a prototype.

Studies have been carried out in the USSR using "weak"

model materials which are intended to reproduce the

properties of those in the prototype (see for example

Rozanov & Rozanova (1981) ).

However t h e p h y s i c a l c h a r a c t e r i s t i c s which c o n t r i b u t e

t o a good c a v i t a t i o n r e s i s t a n c e canno t y e t be

q u a n t i f i e d , p a r t i c u l a r l y i n t h e c a s e of a

non-homogeneous s u b s t a n c e such a s c o n c r e t e . U n t i l

t h i s can be done, mode l l ing of m a t e r i a l s w i l l remain

f a i r l y q u a l i t a t i v e .

Although c a v i t a t i o n t u n n e l s and vacuum t e s t r i g s

e n a b l e models t o be o p e r a t e d a t p r o t o t y p e v a l u e s of K ,

t h e r e s u l t s may s t i l l be s u b j e c t t o s c a l e e f f e c t s .

Such models g e n e r a l l y i n d i c a t e c o r r e c t l y t h e p o i n t s a t

which c a v i t a t i o n w i l l occur i n a p r o t o t y p e . However,

t h e r e is c o n f l i c t i n g ev idence a b o u t whether t h e v a l u e

of a pa ramete r such a s t h e l i m i t of i n c i p i e n t

c a v i t a t i o n K i s a f f e c t e d by t h e p r e s s u r e , v e l o c i t y i

and s c a l e a t which t h e t e s t s a r e c a r r i e d o u t .

Rober tson (1963) sugges ted t h a t i n t h e c a s e of b l u f f

b o d i e s t h e v a l u e of K i s i n i t i a l l y e q u a l t o t h e i

minimum v a l u e of t h e p r e s s u r e c o e f f i c i e n t on t h e

s u r f a c e of t h e body ( i . e . K = -C s e e E q u a t i o n i pm'

B . 2 ) , and t h a t i t i n c r e a s e s a s t h e l o g of t h e Reynolds

number. For s t r e a m l i n e d shapes K s t a r t s below -C i Pm

and r i s e s a s y m p t o t i c a l l y towards t h i s v a l u e a s vSL i n c r e a s e s (where L i s t h e c h a r a c t e r i s t i c l e n g t h ) .

S e v e r a l l a b o r a t o r y s t u d i e s u s i n g models of d i f f e r e n t

s c a l e s have i n d i c a t e d t h a t K. i n c r e a s e s w i t h s i z e , b u t 1

i s n o t a f f e c t e d by changes i n p r e s s u r e o r f low

v e l o c i t y . Examples mentioned i n S e c t i o n B.3 and

Appendix D i n c l u d e c a v i t a t i o n i n o r i f i c e s (see T u l l i s

6 Govindara jan (1973) ), sudden en la rgements a all e t

a 1 (1975) ) and 90' bends ( ~ u l l i s (1981) ). The f a c t

t h a t K v a r i e d w i t h s i z e b u t no t v e l o c i t y i n d i c a t e s i

t h a t t h e s c a l e e f f e c t s i n t h e s e c a s e s were n o t

de te rmined s imply by t h e Reynolds number.

Liu (1984) considered the stresses causing a cavity to

expand or contract, and thereby developed a

theoretical equation which describes the effect of

scale changes on the cavitation parameters. Let the

geometric scale of a model be l:s, and the values of K

measured in the model for incipient and desinent

cavitation be (K ) and (K ) respectively. The i m d m

equation suggests that the prototype values of Ki and

K are given approximately by: d

Interestingly, the theoretical results suggest that

conditions for desinent cavitation are not subject to

significant scale effect. However, the equations have

not been checked against experimental data.

Keller (1984) studied scale effects for incipient

cavitation around axially-symmetric bodies. The

following relationship was found between values of K i

for two bodies of similar shape but different size D

where the factor $varies between about 1.1 for bodies

with streamlined upstream ends and 1.45 for bodies

with blunt ends. Changes in velocity altered the

values of K for the bluff bodies but not for the i

streamlined ones.

It seems possible that the scale effects identified in

studies such as these may be linked to the way in

which the limits of cavitation are identified. A

visual determination of incipient cavitation usually

depends upon t h e s i z e a t which c a v i t i e s can f i r s t be

s e e n by t h e human eye; a l t e r n a t i v e l y t h e l i m i t may be

based upon a c e r t a i n l e v e l o r f requency of c a v i t a t i o n

n o i s e . These c r i t e r i a a r e normal ly k e p t c o n s t a n t , b u t

i n f a c t t h e y ought t o be v a r i e d a c c o r d i n g t o t h e s c a l e

of t h e model: f o r example, l i m i t i n g c a v i t y s i z e

p r o p o r t i o n a l t o model s i z e , o r n o i s e i n t e n s i t y

p r o p o r t i o n a l t o f low energy. Suppor t f o r t h i s

c o n t e n t i o n i s p rov ided by t h e r e s u l t s

of B a l l e t a 1 (1975) Eor sudden en la rgements . A s

ment ioned above, K. (based on n o i s e l e v e l s ) v a r i e d 1

w i t h s i z e , bu t n o t w i t h v e l o c i t y and p r e s s u r e . Values

of t h e pa ramete r K f o r t h e s t a r t of c a v i t a t i o n i d

damage were a l s o measured, u s i n g t h e r a t e of p i t t i n g

p e r u n i t a r e a a s t h e c r i t e r i o n . The r e s u l t s showed

t h a t Kid was not dependent upon s i z e , b u t d i d vary

w i t h p r e s s u r e . The l a c k of s i z e e f f e c t may be because

t h e c r i t e r i o n c o r r e c t l y a l lowed f o r t h e change i n

s c a l e by u s i n g t h e number of p i t s p e r u n i t a r e a r a t h e r

than t h e t o t a l number oE p i t s .

Arndt (1981) s u g g e s t e d t h a t c a v i t a t i o n i n t u r b u l e n t

s h e a r f lows is s u b j e c t t o s c a l e e f f e c t s f o r two

r e a s o n s . F i r s t l y , a s t h e s c a l e i n c r e a s e s , n u c l e i

become r e s p o n s i v e t o a wider range of p r e s s u r e

f l u c t u a t i o n s . Secondly , t h e d e v i a t i o n s Erom mean

p r e s s u r e become l a r g e r a s t h e Reynolds number

i n c r e a s e s . I n f o r m a t i o n on t u r b u l e n c e i n s h e a r f l o w s

i s l i m i t e d , bu t measurements i n d i c a t e t h a t t h e

p r e s s u r e f l u c t u a t i o n s cor respond ing t o g i v e n v e l o c i t y

f l u c t u a t i o n s a r e l a r g e r t h a n occur i n i s o t r o p i c

t u r b u l e n c e .

Hammitt (1975a) surveyed t h e problem of s c a l e e f f e c t s

i n c a v i t a t i o n t e s t i n g , i n c l u d i n g t h o s e due t o changes

i n t e m p e r a t u r e , f l u i d d e n s i t y and v i s c o s i t y , b u t was

n o t a b l e t o draw any f i r m c o n c l u s i o n s .

Evidence from prototype installations is more

encouraging, and suggests that models can correctly

predict the occurrence and extent of cavitation damage

at local features such as gates, baffle blocks and

surface irregularities. Scale effects are difficult

to identify precisely, but models do not appear to

have under-estimated the danger of cavitation in

prototypes. However, the comparisons may not be

conclusive because cavitation is not usually

identified in a prototype until damage occurs (i.e.

K <Kid), whereas most model studies use incipient

cavitation as the design criterion (K >,Ki >Kid).

6 . 2 Air entrainment The fact that water will not entrain air unless the

velocity and turbulence of the flow are great enough

demonstrates clearly that prototype air demands can be

underestimated by models which are too small.

However, it is necessary to distinguish between air

which is entrained into the flow and air which is

drawn along above the free surface. The former is the

phenomenon which needs to be reproduced correctly for

flows on spillways, and at aerators and hydraulic

jumps. The flow of air above the free surface is

important, however, in tunnels because it makes up a

significant proportion of the total air demand.

Laboratory measurements by Ervine et a1 (1980) on

falling jets showed that the minimum velocity required

to entrain air varied from 0.8mIs at a turbulence

level of 8% to 2.51~1~ at a level of 1%. By contrast,

Bruschin (1985) analysed prototype data for the

aerators at Foz do Areia Dam, and estimated the

minimum velocity for entrainment to be 11.3mIs.

The following non-dimensional criteria for the start

of air entrainment have been described earlier in this

review:

s e l f - a e r a t i o n on I, > 56, Equa t ion F . l l s p i l l w a y s

s e l f - a e r a t i o n i n F, > 6 , Equa t ion F.21 p i p e s

a e r a t o r s W e > 1000, Equa t ion F.38

a e r a t o r s F > F k , E q u a t i o n F . 4 5

a e r a t o r s F > 5.8, Equa t ion F.48

S e l f - a e r a t i o n canno t be reproduced s a t i s f a c t o r i l y i n

complete models of dam s p i l l w a y s because i t i s n o t

p o s s i b l e t o s c a l e t h e i n c e p t i o n l e n g t h s c o r r e c t l y and

because t h e v e l o c i t i e s a r e no t u s u a l l y h i g h enough.

However, n u m e r i c a l models based on p r o t o t y p e d a t a .

s u c h a s t h o s e deve loped by Wood (1985) and Ackers &

P r i e s t l e y (1985) ( s e e S e c t i o n F .3 ) , o f f e r a means of

e s t i m a t i n g whether t h e c o n c e n t r a t i o n of e n t r a i n e d a i r

n e a r t h e bed of a channe l w i l l be s u f f i c i e n t t o

p r e v e n t c a v i t a t i o n damage.

L a r g e r - s c a l e models of p a r t i c u l a r p a r t s of dams, s u c h

a s a e r a t o r s and ga ted t u n n e l s , have been used t o

e s t i m a t e p r o t o t y p e a i r demands. The c a s e of g a t e d

t u n n e l s w i l l be c o n s i d e r e d f i r s t .

Harshbarger e t a 1 (1977) c a r r i e d o u t 1:20 s c a l e model

and p r o t o t y p e t e s t s on a t u n n e l f lowing p a r t - f u l l , and

d i d n o t f i n d any s c a l e e f f e c t s i n t h e measured a i r

demands. G a l p e r i n et a 1 (1977) a l s o g i v e d a t a which

showed t h a t a 1:20 model of a g a t e d t u n n e l w i t h f r e e

o u t f l o w s a t i s f a c t o r i l y p r e d i c t e d t h e amount of a i r

e n t r a i n e d i n t h e p r o t o t y p e . The v e l o c i t y of t h e w a t e r

i n t h e model was 6 . 5 ~ 1 1 ~ .

Fa lvey (1980) s u g g e s t s t h a t models can be used

s u c c e s s f u l l y provided a l l t h e a i r - and water-flow

passages a r e c o r r e c t l y reproduced. It i s p a r t i c u l a r l y

i m p o r t a n t t o o b t a i n t h e c o r r e c t head- loss

c h a r a c t e r i s t i c s f o r t h e a i r - s u p p l y system. I f i t s

d e s i g n h a s n o t been de te rmined a t t h e t ime of t e s t i n g ,

t h e performance of t h e model should be measured f o r a

r ange of p o s s i b l e c h a r a c t e r i s t i c s .

Abelev e t a1 (1983) compared model and p r o t o t y p e

measurements of a i r demand i n two ga ted t u n n e l s , each

equipped w i t h a n a e r a t o r . The s c a l e s of t h e models

were 1:34 and 1:36, and i t w a s found t h a t t h e

p r e d i c t e d a i r f low r a t e s (based on Froud ian s c a l i n g )

v a r i e d from abou t 25% t o 50% of t h o s e i n t h e

p r o t o t y p e s .

Vernet h L a r r e a (1985) c o n s i d e r t h a t a i r demand i n

t u n n e l s can be p r e d i c t e d s a t i s f a c t o r i l y p rov ided t h e

s c a l e of t h e model i s n o t l e s s t h a n a b o u t 1 :30. Model

t e s t s were c a r r i e d o u t f o r a f r e e - f l o w i n g t u n n e l

equipped w i t h a n a e r a t o r ; t h e f low t o t h e a e r a t o r was

a s s e s s e d t o be a b o u t 20% of t h e t o t a l a i r demand.

Using a model s c a l e of 1:25, i t was found t h a t t h e

p r e d i c t e d f low r a t e s of a i r were a b o u t 90% of t h o s e i n

t h e p r o t o t y p e .

Evidence from s t u d i e s of a e r a t o r s s u g g e s t s t h a t t h e y

need t o be modelled a t l a r g e r s c a l e s t h a n g a t e d

t u n n e l s i n o r d e r t o g i v e r e l i a b l e e s t i m a t e s of a i r

demand. A e r a t o r s e n t r a i n a i r s t r o n g l y when t h e w a t e r

s u r f a c e above t h e c a v i t y b r e a k s up i n t o a s p r a y ; i t i s

l i k e l y t h a t a h i g h e r v e l o c i t y and l e v e l of t u r b u l e n c e

a r e r e q u i r e d t o produce t h i s s p r a y t h a n t o draw a i r

a l o n g a t u n n e l f l o w i n g p a r t l y f u l l . A e r a t o r s a r e

normal ly t e s t e d u s i n g s e c t i o n a l models , b u t i n

r e l a t i v e l y narrow f lumes t h e boundary l a y e r s on t h e

w a l l s may have a d i s p r o p o r t i o n a t e e f f e c t on t h e amount

of e n t r a i n m e n t .

Data from 1:6 and 1:25 s c a l e models of an a e r a t o r a r e

p r e s e n t e d by G a l p e r i n e t a 1 (1977) . A t low

d i s c h a r g e s , t h e a i r demand i n t h e 1 :6 model was up t o

t w i c e t h a t i n t h e 1:25 model, b u t a t h i g h e r d i s c h a r g e s

t h e two models gave s i m i l a r r e s u l t s .

Q u i n t e l a (1980) d e s c r i b e s Russ ian s t u d i e s c a r r i e d o u t

i n connec t ion w i t h Nurek Dam (USSR). E i g h t a e r a t o r s

were f i t t e d t o a t u n n e l d i s c h a r g i n g on t o a c h u t e

s p i l l w a y . T e s t s of a 1 :35 s c a l e model p r e d i c t e d a i r

demands t h a t were o n l y abou t 20-254 of t h o s e

s u b s e q u e n t l y measured i n t h e p r o t o t y p e .

P i n t o S N e i d e r t (1982) i n v e s t i g a t e d t h e e f f e c t of

s c a l e when s t u d y i n g a e r a t o r s f o r Foz do A r e i a Dam

( B r a z i l ) . S e c t i o n a l models were t e s t e d i n a 150mm

wide f lume a t s c a l e s of 1:50, 30. 15 and 8 ; a l s o a

1:30 g e n e r a l model was used t o r eproduce one h a l f of

t h e p r o t o t y p e s p i l l w a y which i s 70.6m wide. The

p r e d i c t e d a i r demands (based on Froudian s c a l i n g ) i n

t h e 1:8 and 1:15 models were found t o be i n good

agreement w i t h measurements made i n t h e p r o t o t y p e .

The 1:30 and 1:50 models underes t ima ted t h e

e n t r a i n m e n t , bu t t h e d i f f e r e n c e s r e l a t i v e t o t h e

p r o t o t y p e became s m a l l e r a s t h e w a t e r d i s c h a r g e

i n c r e a s e d . However, t h e r e s u l t s a l s o show t h a t t h e

1 :30 g e n e r a l model gave a i r demands t h a t were o n l y 40%

of t h o s e i n t h e 1:30 s e c t i o n a l model. T h i s s u g g e s t s

t h a t t h e agreement between t h e two l a r g e r s c a l e

s e c t i o n a l models and t h e p r o t o t y p e may have been

enhanced by i n c r e a s e d e n t r a i n m e n t a t t h e s i d e w a l l s of

t h e f lume.

Z a g u s t i n e t a 1 (1982) and Zagus t in S C a s t i l l e j o (1983)

c a r r i e d o u t compara t ive t e s t s on t h e ramp-type

a e r a t o r s t o be used i n c h u t e no 3 of Guri Dam

( ~ r g e n t i n a ) . S e c t i o n a l models a t s c a l e s of 1:50, 40 ,

30, 25, 1 5 and 10 were i n s t a l l e d i n s e r i e s i n a 300mm

wide flume. P r e d i c t e d a i r demands from t h e 1:10 and

1:15 models were found t o be i n s a t i s f a c t o r y agreement

with p r o t o t y p e measurements, whi le t h e 1:20 model gave

v a l u e s t h a t were about 10% low. S i n c e t h e width o f

each model was t h e same, t h e e f f e c t of t h e s i d e w a l l s

on t h e amount of en t ra inment may have i n c r e a s e d a s t h e

s c a l e became l a r g e r . Measured c a v i t y l e n g t h s i n t h e

1:50 model were found t o be 20-302 g r e a t e r than t h o s e

i n t h e p ro to type ; t h i s was due t o t h e f a c t t h a t t h e

amount of s u c t i o n a t t h e a e r a t o r was t o o s m a l l i n t h e

model.

I n connec t ion w i t h s t u d i e s f o r San Roque Dam

( P h i l i p p i n e s ) , Volkar t h Chervet (1983) i n v e s t i g a t e d

s i z e e f f e c t s by t e s t i n g models of an a e r a t o r w i t h a

combined ramp and o f f s e t a t s c a l e s of 1:30, 25, 21.43

and 18.75. Each model r e p r e s e n t e d a p r o t o t y p e w i d t h

of 2.25m, s o t h a t i n t h e t e s t s t h e wid ths v a r i e d from

75mm t o 120mm; t h e p r o p o r t i o n a t e e f f e c t of t h e s i d e

w a l l s t h e r e f o r e remained t h e same i n a l l t h e t e s t s .

P r o t o t y p e d a t a were n o t a v a i l a b l e , s o i t was n o t

p o s s i b l e t o de te rmine t h e o v e r a l l s c a l e e f f e c t s

p r e c i s e l y . However, comparing t h e v a r i o u s r e s u l t s and

e x p r e s s i n g them i n terms of t h e a i r demand i n t h e

1:18.75 model gave t h e f o l l o w i n g f a c t o r s

S c a l e A i r demand r a t i o

106% ( e s t i m a t e d ) 100% 96% 89% 73%

The v a l u e s of t h e r a t i o s v a r i e d somewhat w i t h t h e f l o w

c o n d i t i o n s , and those g iven above a r e t h e mean

f i g u r e s . The maximum a v e r a g e a i r c o n c e n t r a t i o n

achieved i n t h e s e model t e s t s was 5.8%.

Pan h Shao (1984) c a r r i e d o u t t e s t s on two ramp

a e r a t o r s used i n a r e c t a n g u l a r s p i l l w a y t u n n e l

(measur ing 7.2m wide by 11.h h i g h ) a t F e n g j i a s h a n Dam

( C h i n a ) . A model of t h e whole t u n n e l w a s c o n s t r u c t e d

a t a scale of 1 :40 , t o g e t h e r w i t h p a r t i a l models ( e a c h

2OOmm wide) a t s c a l e s of 1:30. 20, 15 and 12. A i r

demands i n t h e p r o t o t y p e t u n n e l were a l s o measured a t

f i v e d i s c h a r g e s up t o 548m3/s, and were found t o v a r y

be tween = 0.15-0.30 f o r Froude numbers o f

F = 6.0-8.5. The r e s u l t s showed t h a t t h e 1:40 a n d

1 :30 models u n d e r e s t i m a t e d t h e a i r demands, b u t t h a t

t h e l a r g e r models a g r e e d q u i t e w e l l . From t h e tests

i t was conc luded t h a t a model of a n a e r a t o r w i l l

p r e d i c t t h e a i r demand c o r r e c t l y i f t h e f o l l o w i n g

l i m i t s are s a t i s f i e d

where L i s t h e l e n g t h of t h e a i r c a v i t y . I t was a l s o C

c o n s i d e r e d t h a t a model which meets t h e s e r e q u i r e m e n t s

w i l l n o t b e s u b j e c t t o s c a l e e f f e c t s due t o s u r f a c e

t e n s i o n . However, problems do r ema in i n m o d e l l i n g

c o r r e c t l y how t h e a i r i n t r o d u c e d by a n a e r a t o r

d i f f u s e s i n t o t h e f l o w downstream o f t h e p o i n t o f

r e a t t a c h m e n t .

V o l k a r t h Rutschmann (1984b) measured a i r e n t r a i n m e n t

i n a small s p i l l w a y a t Grande Dixence power p l a n t

( S w i t z e r l a n d ) ; t h e s p i l l w a y measured 0 . 8 h by 0 .801~

i n s e c t i o n , and tests were c a r r i e d o u t b o t h w i t h and

w i t h o u t a ramp d e f l e c t o r . The r e s u l t s were compared

w i t h measurements i n models w i t h scales v a r y i n g f rom

1 :6 t o 1:18.75. The models were o p e r a t e d s o a s t o

o b t a i n t h e c o r r e c t F r o u d i a n v e l o c i t i e s , bu t n o t

n e c e s s a r i l y t h e c o r r e c t f l o w d e p t h s . A l so , t h e model

c h a n n e l s wee made r e l a t i v e l y w i d e r t h a n i n t h e

p r o t o t y p e s o as t o allow f o r t h e e f f e c t s of w a l l

r oughness . A l l t h e models unde r -e s t ima ted b o t h t h e

jet l e n g t h and t h e a i r demand produced by t h e

prototype aerator. No simple relation was found for

scaling the model results correctly. In order to

minimise modelling errors, the pressure distribution

and velocity profile at the prototype ramp need to be

carefully reproduced in the model.

Sakhuja et a1 (1984) analysed the relationship between

measured air demands in models and prototypes for

aerators and gated tunnels. They found that the scale

effect X (defined as the prototype air demand divided

by the model demand transformed according to the

Froude criterion) was related to the geometric scale s

(prototype/model) by:

log l0 X = 0.0048 (S-l) (G-6)

On the basis of experimental evidence such as that

described in Section F.1, it is generally accepted

that local air concentrations of about 5-10% are

sufficient to prevent damage by collapsing cavities.

However, experiments carried out by Clyde h Tullis

(1983) on cavitation at orifices in pipes suggest that

the limiting air concentration is itself subject to

scale effects. Tests to determine the onset of

cavitation were performed first without the addition

of air; the limit was detected by a sudden change in

the level of turbulence. Air was then injected, and

the velocity increased until the level of turbulence

was the same as it was at the onset of cavitation

without air. The results showed that, for a given

flow velocity and orifice ratio, the amount of air

needed decreased rapidly with pipe size : for example

at V = 2.33m/s, the concentration required in a 76mm

diameter pipe was C = 6.1% whereas in a 610mm pipe it

was C = 0.16%. Using as a parameter the rate of air

flowlunit length of perimeter correlated the data

better than did the concentration. It was also found

that the required amount of air increased considerably

as the flow velocity was increased.

G.3 Instrumentation Specialised instruments are needed to study aerated

for aerated flows. The main quantities to be measured are the air

flows concentration and the velocity of flow. A summary of

some of the techniques is given by Lakshmana Rao h

Kobus .

In the case of concentration, it is necessary to

distinguish between methods which measure the volume

of air bubbles per unit volume of water from those

which record the relative rates of flow of air and

water (see Section F.2). The first group includes

gamma ray attenuation equipment (see for example Babb

h Aus (1981)), instruments which measure the change in

conductivity of water due to the presence of bubbles

(e.g. Cain h Wood (1981a)), and methods based on the

attenuation of a beam of light (see Lakshmana Rao &

Kobus). The second group includes probes used to

abstract samples of air-water mixtures, which are then

separated into their two components. Vischer et a1

(1982) explain how it is necessary to ensure that the

rate of abstraction is equal to the velocity of flow,

which itself partly depends upon the air

concentration; it is therefore necessary to draw off

the samples at several different rates in order to

determine the true flow velocity and air

concentration. Having obtained a sample, the amount

of dissolved air can be found by measuring the

conductivity of the water, which is affected by the

partial pressure of the dissolved oxygen. The total

amount of air (free + dissolved) can be determined using equipment such as the Van Slyke apparatus, or

the newer Brand apparatus described by Mohammad &

Hutton (1986).

A s e p a r a t e c l a s s of i n s t r u m e n t s f o r measur ing

c o n c e n t r a t i o n works by r e c o r d i n g t h e p r o p o r t i o n a t e

l e n g t h s of t i m e t h a t a probe i s i n a i r and i n wa te r .

The s i g n a l may be produced by ho t - f i lm t e c h n i q u e s ( e g

Babb & Aus ( 1 9 8 1 ) ) , o r by t h e change i n r e s i s t a n c e

which o c c u r s when t h e t i p of a n i n s u l a t e d probe p a s s e s

th rough an a i r bubble (White & Hay (1975) ) . These

d e v i c e s i n f a c t f u n c t i o n by d e t e c t i n g t h e a i r - w a t e r

i n t e r f a c e s , and t h e r e would seem t o be a problem of

d e c i d i n g p r e c i s e l y what q u a n t i t y t h e y a c t u a l l y measure

i f t h e a i r and w a t e r phases do n o t t r a v e l a t t h e same

speed.

Another t y p e of i n s t r u m e n t is t h e twin-wire gauge

deve loped by Halbronn (1951). T h i s c o n s i s t e d of two

0.3mm d i a m e t e r w i r e s i n s u l a t e d from each o t h e r and

t w i s t e d t o form a t h i n tube . The e l e c t r i c a l

r e s i s t a n c e of t h e gauge depends upon t h e p r o p o r t i o n a t e

l e n g t h of t h e t u b e t h a t i s i n c o n t a c t w i t h w a t e r , s o

i n a e r a t e d f l o w t h e r e s i s t a n c e i s d i r e c t l y r e l a t e d t o

t h e a i r c o n c e n t r a t i o n .

Conven t iona l p i t o t t u b e s have been used t o d e t e r m i n e

t h e v e l o c i t y of a e r a t e d f l o w s , and V i s c h e r e t a 1

(1982) found t h a t they were s a t i s f a c t o r y f o r a i r

c o n c e n t r a t i o n s of up t o 10%. Var ious a u t h o r s have

d i f f e r e d on how r e s u l t s from p i t o t t u b e s shou ld be

i n t e r p r e t e d ( s e e Lakshmana Rao & Kobus) : t h e problems

c e n t r e on how t h e d e n s i t y and v e l o c i t y of a i r - w a t e r

m i x t u r e s shou ld be d e f i n e d . C a i n & Wood (1981a) show

t h a t t h e p resence of a i r i n wa te r c a n reduce t h e speed

of sound i n t h e m i x t u r e t o t h e o r d e r of 20m/s, s o t h a t

c o m p r e s s i b i l i t y e f f e c t s may need t o be t a k e n i n t o

accoun t when a n a l y s i n g d a t a from p i t o t t u b e s .

An a l t e r n a t i v e method f o r d e t e r m i n i n g v e l o c i t y i s t o

measure t h e t ime d e l a y between s i g n a l s from two p robes

which respond t o t h e passage of a i r b u b b l e s , and which

are mounted parallel to the flow and a known distance

apart; the time delay is normally obtained by

cross-correlating the two signals. If the probes are

close together, they will respond to the same set of

bubbles, but the time difference will be small. If

the probes are further apart, the time delay can be

measured more accurately, but the correlation will be

determined by larger-scale variations in the flow

rather than by the passage of individual bubbles.

Vischer et a1 (1982) used an instrument with probes

lOmm apart for laboratory work, whereas Cain S Wood

(1981a) adopted a separation of 101.6mm for field

measurements on Aviemore Dam. Cain S Wood argued that

their equipment measured the velocity of water, but

the principle of the method suggests that it does in

fact register the velocity of the air-water

interfaces. When the air concentration is very low,

the velocity of the interfaces is equal to that of the

air bubbles; conversely at very high concentrations,

the velocity is that of the water droplets. When

there are approximately equal volumes of air and water

and the two phases move at different speeds, it is

difficult to determine or define the velocity at which

the interfaces between the air and water will move.

A third method of velocity measurement was used by

Straub & Anderson (1958), and involved injecting a

salt solution into the flow and measuring its time of

travel over a known distance; since the salt is

transported by the water, this technique gives an

estimate of the average water velocity.

APPENDIX E

FUTURE RESEARCH

F u r t h e r r e s e a r c h t h a t would be of b e n e f i t i n t h e

d e s i g n of h y d r a u l i c s t r u c t u r e s w i l l be cons idered

under some of t h e head ings used earlier i n t h i s

review.

1. Mechanism of C a v i t a t i o n

When s t u d i e d i n d e t a i l , a lmos t every a s p e c t of

c a v i t a t i o n i s found t o be i m p e r f e c t l y unders tood.

Fundamental r e s e a r c h , both t h e o r e t i c a l and

e x p e r i m e n t a l , can t h e r e f o r e be expected t o c o n t i n u e i n

u n i v e r s i t i e s on a broad f r o n t . P a r t i c u l a r t o p i c s t h a t

would be r e l e v a n t t o c i v i l e n g i n e e r i n g h y d r a u l i c s

a r e :

( a ) r o l e of n u c l e i i n t h e growth of c a v i t i e s ,

p a r t i c u l a r l y i n l a r g e - s c a l e s t r u c t u r e s such

a s t u n n e l s and s p i l l w a y s ;

( b ) g e n e r a t i o n of c a v i t i e s i n t u r b u l e n t s h e a r

f l o w s ;

( C ) mot ion of c a v i t i e s and mechanisms of

c o l l a p s e ;

( d ) p r e s s u r e s and f o r c e s produced by c a v i t i e s

c o l l a p s i n g n e a r s o l i d boundar ies ;

( e ) c o n c e n t r a t i o n of a i r needed t o p reven t

c a v i t a t i o n damage, and v a r i a t i o n of requ i red

c o n c e n t r a t i o n wi th v e l o c i t y and s c a l e .

2. C a v i t a t i o n a t S u r f a c e Irregularities

A c o n s i d e r a b l e amount of l a b o r a t o r y work h a s been

c a r r i e d o u t on c a v i t a t i o n a t v a r i o u s t y p e s of

i r r e g u l a r i t y . I n g e n e r a l , v a l u e s o b t a i n e d by

d i f f e r e n t r e s e a r c h e r s f o r t h e i n c i p i e n t c a v i t a t i o n

index K . a r e i n r e a s o n a b l e agreement , and e n a b l e 1

d e s i g n e r s t o assess t h e l i k e l i h o o d of damage and t o

s p e c i f y s u i t a b l e t o l e r a n c e s f o r s u r f a c e f i n i s h . Some

u n c e r t a i n t i e s i n t h e r e s u l t s remain, f o r example

whether t h e v a l u e of K f o r a chamfer depends upon i t s i h e i g h t a s w e l l a s i t s s l o p e . However, i t i s u n l i k e l y

t h a t f u r t h e r t e s t i n g would r e s o l v e t h e s e q u e s t i o n s

e n t i r e l y because of t h e d i f f i c u l t i e s of o b t a i n i n g

e x a c t l y e q u i v a l e n t c o n d i t i o n s i n d i f f e r e n t

l a b o r a t o r i e s ( e g g a s con ten t of t h e w a t e r and t h e

number and s i z e of n u c l e i ) . More i m p o r t a n t l y , t h e

t y p e s of f a u l t which occur i n p r o t o t y p e s t r u c t u r e s

tend t o be i r r e g u l a r and th ree -d imens iona l , and w i l l

seldom cor respond e x a c t l y t o t h o s e t e s t e d i n

l a b o r a t o r i e s . P o s s i b l e a r e a s f o r new r e s e a r c h a r e :

( a ) model and p r o t o t y p e tests t o de te rmine

c o n d i t i o n s f o r t h e s t a r t of c a v i t a t i o n

damage a t s u r f a c e i r r e g u l a r i t i e s ( i e v a l u e s

of K. i n s t e a d of t h e more c o n s e r v a t i v e l d

i n c e p t i o n pa ramete r K . ) ; 1

( b ) s t u d i e s t o i d e n t i f y types of c o n s t r u c t i o n

j o i n t which a r e l e s s l i a b l e t o cause

c a v i t a t i o n problems on s p i l l w a y s .

3. Tunnels and Ga tes

S e v e r a l s t u d i e s have reached s i m i l a r c o n c l u s i o n s abou t

t h e f e a t u r e s of g a t e s l o t s which a r e d e s i r a b l e i n

o r d e r t o minimise t h e danger of c a v i t a t i o n . Although

f u r t h e r r e s e a r c h might p rov ide more d e t a i l e d

recommendations, i c is u n l i k e l y t h a t they would remove

t h e need t o test models of ma jor s t r u c c u r e s , s i n c e

each scheme t e n d s t o have s p e c i a l r equ i rements t h a t

p r e v e n t t h e a d o p t i o n of s t a n d a r d d e s i g n s . Topics

which war ran t f u r t h e r i n v e s t i g a t i o n are:

(a) a l t e r n a t i v e g a t e d e s i g n s which would

e l i m i n a t e t h e need f o r s l o t s on t h e

downstream s i d e ;

( b ) new m a t e r i a l s f o r l i n i n g t u n n e l s a s cheaper

a l t e r n a t i v e s t o s t a i n l e s s s t e e l .

4. Energy D i s s i p a t o r s

Outs ide of t h e USSR, l i t t l e r e s e a r c h a p p e a r s t o have

been c a r r i e d o u t on t h e d e s i g n of s u p e r c a v i t a t i n g

b a f f l e b l o c k s f o r s t i l l i n g b a s i n s . The reasons f o r

t h i s a r e no t e v i d e n t from t h e l i t e r a t u r e , but i t cou ld

be because: (1) wes te rn d e s i g n e r s avo id t h e use of

appur tenances i n high-head s t i l l i n g b a s i n s ; ( 2 ) i n

such s i t u a t i o n s they choose a l t e r n a t i v e t y p e s of

ene rgy d i s s i p a t o r ; (3) f low a e r a t i o n i s normal ly

s u f f i c i e n t t o p r e v e n t c a v i t a t i o n damage a t t h e f o o t of

s p i l l w a y s . B a f f l e b locks pe rmi t s h o r t e r s t i l l i n g

b a s i n s , and t h e i r i n c r e a s e d u s e could produce c o s t

s a v i n g s . Views should t h e r e f o r e be sought from t h e

c i v i l e n g i n e e r i n g p r o f e s s i o n abou t t h e need f o r :

( a ) Research on t y p e s of s u p e r c a v i t a t i n g b a f f l e

b lock f o r u s e i n h y d r a u l i c jump s t i l l i n g

b a s i n s .

I n o r d e r t o reproduce f r e e - s u r f a c e e f f e c t s c o r r e c t l y ,

t h i s work would need t o be c a r r i e d o u t i n a vacuum

t e s t r i g , which t h e UK does no t a t p r e s e n t p o s s e s s .

5. M a t e r i a l s

R e s u l t s from c a v i t a t i o n t e s t i n g of m a t e r i a l s tend t o

be a f f e c t e d by t h e type of equipment used and t h e

p a r t i c u l a r l a b o r a t o r y c o n d i t i o n s . It i s t h e r e f o r e

recogn i sed t h a t such s t u d i e s do no t g i v e very p r e c i s e

e s t i m a t e s of how much damage can be expec ted t o o c c u r

i n a p r o t o t y p e . However, comparat ive t e s t s c a r r i e d

o u t under s i m i l a r c o n d i t i o n s do a s s i s t d e s i g n e r s t o

choose between d i f f e r e n t m a t e r i a l s accord ing t o t h e

p e r c e i v e d l e v e l of c a v i t a t i o n r i s k . Such work h a s

been c a r r i e d o u t f o r a wide range of s t e e l s , but t h e r e

a r e r e l a t i v e l y few r e s u l t s f o r c o n c r e t e and t h e s e a r e

d i f f i c u l t t o compare. There i s t h e r e f o r e a

requirement f o r:

( a ) s y s t e m a t i c s t u d i e s t o e s t a b l i s h a

comparat ive s c a l e of c a v i t a t i o n r e s i s t a n c e

f o r a range of o r d i n a r y c o n c r e t e s , s p e c i a l

c o n c r e t e s (eg s t e e l - f i b r e and epoxy

c o n c r e t e s ) and epoxy f i l l e r s . The method

used s h o u l d reproduce a s c l o s e l y a s p o s s i b l e

t h e t y p e of c a v i t a t i o n which o c c u r s i n

p r o t o t y p e s t r u c t u r e s : vor tex-shedding

t e c h n i q u e s a r e t h e r e f o r e p r e f e r a b l e t o

v i b r a t o r y o r drop-impact methods.

6. S e l f - A e r a t i o n

S e l f - a e r a t i o n on s p i l l w a y s i s impor tan t i n i t s own

r i g h t , and i n r e l a t i o n t o c a v i t a t i o n because t h e

p r e s e n c e of e n t r a i n e d a i r i n a f low may p reven t damage

from c o l l a p s i n g c a v i t i e s . It i s not f e a s i b l e t o

p r e d i c t s e l f - a e r a t i o n by means of p h y s i c a l models, and

t h e b e s t way forward a p p e a r s t o be t h e development of

numerical models based on l a b o r a t o r y and p r o t o t y p e

i n f o r m a t i o n . A t p r e s e n t t h e amount of e x p e r i m e n t a l

d a t a i s l i m i t e d , and covers on ly a l i m i t e d range of

u n i t d i s c h a r g e s ( < 3.2m 3/s p e r m). The f o l l o w i n g work

i s t h e r e f o r e needed:

( a ) measurements of a e r a t e d f lows on p r o t o t y p e

s p i l l w a y s f o r u n i t d i s c h a r g e s g r e a t e r t h a n

5m3/s p e r me t re wid th of channe l .

It i s a p p r e c i a t e d t h a t t h i s p r o p o s a l would be

d i f f i c u l t and expens ive t o a c h i e v e , b u t w i t h o u t such

d a t a i t w i l l n o t be p o s s i b l e t o v e r i f y numer ica l

models and o b t a i n r e l i a b l e p r e d i c t i o n s f o r

h i g h - d i s c h a r g e s p i l l w a y s .

7. A e r a t i o n i n Tunne l s

Comparative d a t a from model and p r o t o t y p e t e s t s on

g a t e d t u n n e l s i n d i c a t e t h a t c a r e f u l l y - c o n s t r u c t e d

models of s u i t a b l e s c a l e can g i v e s a t i s f a c t o r y

e s t i m a t e s of a i r demand. A number of e q u a t i o n s f o r

p r e d i c t i n g a i r demand a r e a v a i l a b l e , bu t g i v e

c o n t r a d i c t o r y e s t i m a t e s . Before any new b a s i c

r e s e a r c h i s c a r r i e d o u t , i t i s recommended t h a t :

( a ) a v a i l a b l e model and p r o t o t y p e i n f o r m a t i o n on

g a t e d t u n n e l s shou ld be c r i t i c a l l y reviewed

i n o r d e r t o d e t e r m i n e whether s u f f i c i e n t

d a t a a l r e a d y e x i s t t o make r e l i a b l e

p r e d i c t i o n s of a i r demand.

8. A e r a t o r s

A e r a t o r s a r e b e i n g i n c r e a s i n g l y used t o p r e v e n t

c a v i t a t i o n damage i n t u n n e l s and s p i l l w a y s .

I n t h e c a s e of t u n n e l s , some g e n e r a l recommendations

have been produced f o r t h e d e s i g n of a e r a t o r s

i n c o r p o r a t i n g f l o o r - and w a l l - d e f l e c t o r s . However i t

i s l i k e l y t h a t model t e s t s w i l l c o n t i n u e t o be needed

because smal l v a r i a t i o n s i n g a t e c o n f i g u r a t i o n can

s i g n i f i c a n t l y a l t e r t h e f low c o n d i t i o n s a t a n

a e r a t o r .

I n t h e c a s e of s p i l l w a y s , model s t u d i e s f o r i n d i v i d u a l

schemes have l e d t o t h e u s e of a v a r i e t y of d i f f e r e n t

t y p e s of a e r a t o r . However, s i n c e flow c o n d i t i o n s i n a

s p i l l w a y can be d e f i n e d i n terms of a few v a r i a b l e s

( e g v e l o c i t y , dep th and channe l s l o p e ) , a s y s t e m a t i c

programme of r e s e a r c h shou ld e n a b l e t h e most e f f e c t i v e

c o n f i g u r a t i o n s t o be i d e n t i f i e d . I t shou ld a l s o be

p o s s i b l e t o d e f i n e s t a n d a r d d e s i g n s whose dimensions

cou ld be s e l e c t e d accord ing t o t h e p a r t i c u l a r f l o w

c o n d i t i o n s on a s p i l l w a y . T h i s would reduce t h e c o s t s

of i n d i v i d u a l model s t u d i e s of dams, and would make

e f f i c i e n t u s e of p r o t o t y p e d a t a , s i n c e t h e performance

of a e r a t o r s on d i f f e r e n t dams cou ld be compared on a

s i m i l a r b a s i s a g a i n s t r e s u l t s from t h e l a b o r a t o r y

s t u d i e s . O b j e c t i v e s of a n i n t e g r a t e d programme of

e x p e r i m e n t a l r e s e a r c h shou ld be t o determine:

( a ) l e n g t h oE a i r c a v i t y formed a t an a e r a t o r a s

a f u n c t i o n of ( i ) f low c o n d i t i o n s , ( i i )

geometry of t h e a e r a t o r , and ( i i i ) head- loss

c h a r a c t e r i s t i c s of t h e a i r supp ly system;

( b ) most s u i t a b l e t h e o r e t i c a l method f o r

p r e d i c t i n g l e n g t h of a i r c a v i t y ;

( C ) r e l a t i o n s h i p between a i r demand, c a v i t y

l e n g t h and f low c o n d i t i o n s a t a e r a t o r ;

( d ) e f f e c t on a i r demand of changes i n s c a l e ;

( e ) e f f e c t of s i d e w a l l s on a i r demand;

( f ) e f f e c t of a e r a t o r s on a e r a t i o n a t f r e e

s u r f a c e ;

'SlOJ81aE

JO maaxJsunop MOT$ moxj lye 30 ss01 30 aJsl (q)

APPENDIX I

REFERENCES

Abbreviations

ASCE - American Society of Civil Engineers ASME - American Society of Mechanical Engineers BHRA - British Hydromechanics Research Association CIRIA - Construction Industry Research and Information

Association

DFG - Deutsche Forschungsgemeinschaft DVWK - Deutscher Verband fsr Wasserwirtschaft und

Kulturbau e.V.

ETH - Eidgenksischen Technischen Hochschule

ICE - Institution of Civil Engineers ICOLD - International Commission on Large Dams ISCME - Internation Society of Computational Methods

in Engineering

IWHR - Institute of Water Conservancy and Hydroelectric Power Research

Abelev A S et a1 (1971). Investigation of relative

cavitation resistance of materials and protective

coatings and development of measures against

cavitation erosion of hydraulic structure elements.

Proc XIVth IAHR Congress, Paris, Vol 5, pp 69-72.

Abelev A S et a1 (1983). Methodes de calcul de

l'aeration d'un ecoulement dans les projets de

deversoirs. Proc XXth IAHR Congress, Moscow, Vol 7,

pp 361-365.

Ackers P h Priestley S J (1985). Self-aerated flow

down a chute spillway. 2nd Intern Conf on Hydraulics

of Floods and Flood Control, BHRA, Cambridge, England,

pp 1-16.

Adami A (1974). Experimental study of flow near the

slots of gates in deep outlets, in regard to possible

cavitation phenomena. Hydraulic Institute, University

of Padua, Studi e Ricerche 301 (in Italian).

Ahmed A A et a1 (1984). The process of aeration in

closed conduit hydraulic structures. Symp on Scale

Effects in Modelling Hydraulic Structures, IAHRIDVWK, Esslingen, FR Germany, September, Paper 4.13

Akbari M E et a1 (1982). Pressure fluctuations on the

floor of free and forced hydraulic jumps. Intern Conf

on Hydraulic Modelling of Civil Engineering

Structures, BHRA, Coventry, pp87-96.

Aksoy S h Etembabaoglu S (1979). Cavitation damage at

the discharge channels of Keban Dam. 13th ICOLD

Congress, New Delhi, Vol 111, Q50, R21, pp 369-379.

American Concrete Institute. Erosion of concrete in

hydraulic structures. Prepared by ACI Committee 210.

To be published.

ASCE Task Committee (1961). Aerated flow in open

channels. Proc ASCE, Jnl Hydr Div, Vol 87, HY3, May,

pp73-86.

Anderson A G (1965). Influence of channel roughness

on the aeration of high velocity, open-channel flow.

Proc XIth IAHR Congress, Leningrad, Vol 1, Paper 37.

Arndt R E A (1981). Cavitation in fluid machinery and

hydraulic structures. Annual Review of Fluid Mech,

Vol 13, Annual Reviews Inc, Pal0 Alto, California,

pp 273-328.

Arndt R E A et a1 (1979). Influence of surface

irregularities on cavitation performance. Jnl Ship

Research, Vol 23, No 3, September, pp 157-170.

Babb A F h Aus H C (1981). Measurement of air in

flowing water. Proc ASCE, Jnl Hydr Div, Vol 107,

HY12, December, pp 1615-1630.

Ball J W (1959). Hydraulic characteristics of gate

slots. Proc ASCE, Jnl Hydr Div, Vol 8 5 , HY10,

October, Part 1, pp 81-114.

Ball J W (1963). Construction finishes and

high-velocity flow. Proc ASCE, Jnl Constr Div, Vol

89, C02, September, pp 91-110.

Ball J W et a1 (1975). Predicting cavitation in

sudden enlargements. Proc ASCE, Jnl Hydr Div,

Vol 101, HY7, July, pp 857-870.

Barletta A & Ball A (1983). Cavitation erosion of

polymeric materials. Proc 6th Intern Conf on Erosion

by Liquid and Solid Impact, Cambridge, England,

Paper 1.

Batchelor G K (1967). An Introduction to Fluid

Mechanics. Cambridge Univ Press.

Bauer W J (1954). Turbulent boundary layer on steep

slopes. Trans ASCE, Vol 119, pp 1212-1233.

Beichley G L & King D L (1975). Cavitation control by

aeration of high-velocity jets. Proc ASCE, Jnl Hydr

Div, Vol 101, HY7, July, pp 829-845.

Billore J et a1 (1979). Recherches hydrauliques pour

la dsrivation provisoire, les dgversoirs en puits et

la vidange de fond du barrage de M'Dez au Maroc. 13th

ICOLD Congress , New D e l h i , Vol 111, Q50, R62,

pp 1085-1106.

Bowers C E h T s a i F Y (1969) . F l u c t u a t i n g p r e s s u r e s

i n s p i l l w a y s t i l l i n g b a s i n s . P roc ASCE, J n l Hydr Div,

Vol 95, HY6, November. pp 2071-2080.

B r e t s c h n e i d e r H (1986) . The beg inn ing of a i r

e n t r a i n m e n t a t bottom grooves . Sonnderdruck a u s

W a s s e r w i r t s c h a f t , H e f t 5, Franckh-Kosmos, S t u t t g a r t

( i n German).

Brusch in J (1982). Air -water f low on s p i l l w a y s and i n

plugged bottom o u t l e t s . I n t e r n Conf on H y d r a u l i c

Model l ing of C i v i l Eng ineer ing S t r u c t u r e s , BHRA,

Coventry , pp 215-222.

Brusch in J (1985) . H y d r a u l i c mode l l ing a t t h e P i e d r a

d e l Agui la dam. Water Power h Dam C o n s t r u c t i o n ,

Vol 37, J a n u a r y , pp 24-28.

Brusch in J (1987). Forced a e r a t i o n of h igh v e l o c i t y

f l o w s . J n l Hydr Res, Vol 25, No l , pp5-14.

Ca in P h Wood I R (1981a) . I n s t r u m e n t a t i o n f o r

a e r a t e d f low on s p i l l w a y s . P roc ASCE, J n l Hydr Div,

Vol 107. H Y 1 1 , November, pp 1407-1424.

C a i n P h Wood I R (1981b) . Measurements of

s e l f - a e r a t e d f low on a s p i l l w a y . Proc ASCE, J n l Hydr

Div, Vol 107, H Y l l , November, pp 1425-1424.

Campbell F B h Guyton B (1953). A i r demand i n g a t e d

o u t l e t works. IAHR/ASCE Minnesota I n t e r n H y d r a u l i c s

Convent ion, M i n n e a p o l i s , pp 529-533.

C a s s i d y J J h E l d e r R A (1984). S p i l l w a y s of h i g h

dams. Ch 4 i n Developments i n H y d r a u l i c Eng ineer ing -

2 , ed P Novak, E l s e v i e r Appl S c i P u b l , London,

pp 159-182.

Chao P C (1980) . T a r b e l a dam - problems s o l v e d by

n o v e l c o n c r e t e s . C i v i l E n g i n e e r i n g (ASCE), December,

pp 58-64.

Clyde E S & T u l l i s J P (1983) . A e r a t i o n s c a l e

e f f e c t s . P r o c Con£ on F r o n t i e r s i n H y d r a u l i c

E n g i n e e r i n g , ASCE, Cambridge, USA, p 413-418.

C o l e g a t e D M (1971). H y d r a u l i c model s t u d i e s o f

a e r a t i o n d e v i c e s f o r Y e l l o w t a i l Dam s p i l l w a y t u n n e l ,

Pick-Sloan M i s s o u r i B a s i n Program, Montana. US Bureau

o f Reclamat ion . Repor t REC-ERC-71-47.

C o l e g a t e D (1977) . C a v i t a t i o n damage i n h y d r a u l i c

s t r u c t u r e s . I n t e r n Conf on Wear of M a t e r i a l s , S t

L o u i s , USA.

Coleman H W e t a 1 (1983) . A e r a t i o n f o r c a v i t a t i o n

p r o t e c t i o n of U r i b a n t e S p i l l w a y . P r o c Conf on

F r o n t i e r s i n H y d r a u l i c E n g i n e e r i n g , ASCE, Cambridge,

USA, pp 438-443.

Cui L (1985). A i r c o n c e n t r a t i o n d i s t r i b u t i o n

downstream o f a e r a t i o n ramp. J n l Hydr Engng

( B e i j i n g ) , No 1, pp 45-50 ( i n Ch inese ) .

De F a z i o F G & Wei C Y (1983) . Des ign of a e r a t i o n

d e v i c e s on h y d r a u l i c s t r u c t u r e s . P r o c Con£ on

F r o n t i e r s i n H y d r a u l i c E n g i n e e r i n g , ASCE, Cambridge ,

USA, pp 426-431.

De F a z i o F G h Wei C Y (1985) . Correspondence i n

Water Power h Dam C o n s t r u c t i o n , Vol 37 , December,

P 6 -

Dejoux A e t a 1 (1983). Concep t ion d e s o u v r a g e s

d ' e v a c u a t i o n d e s c r u e s e t d e v idange d u b a r r a g e d e

S o u a p i t i (GuinCe). La H o u i l l e B lanche , NumCro 3-4,

pp 221-230.

Demiroz E h Acatay T (1985) . I n f l u e n c e of c h a m f e r s

away from f l o w on c a v i t a t i o n i n c e p t i o n . P r o c X X I s t

IAHR Congress , Melbourne , Seminar 2.

Des tenay J S Bernard J (1968) . Quelques exemples d e

d e g r a d a t i o n d e s b 6 t o n s p a r c a v i t a t i o n d a n s d e s

ouvrages h y d r o C l e c t r i q u e s . La H o u i l l e B lanche ,

Num&ro 2-3, pp 167-176.

Duncan W J e t a 1 (1962) . The Mechanics o f F l u i d s .

Edward Arno ld ( P u b l i s h e r s ) L i m i t e d , London.

Eccher L h S i e g e n t h a l e r A (1982) . S p i l l w a y a e r a t i o n

o f t h e San Roque p r o j e c t . Water Power h Dam

C o n s t r u c t i o n , Vol 34 , September , pp 37-41.

E i s e n b e r g P (1961) . C a v i t a t i o n . S e c t i o n 12 i n

Handbook of F l u i d Dynamics, ed V L S t r e e t e r ,

McGraw-Hill Book C O , New York, pp 12/1-46.

E r v i n e D A e t a 1 (1980) . Model -proto type c o n f o r m i t y

i n h y d r a u l i c s t r u c t u r e s i n v o l v i n g a e r a t i o n . P r o c

XIXth IAHR Congress , New D e l h i , Vol 5, pp 65-72.

Ethembabaoglu S (1978) . Some c h a r a c t e r i s t i c s of

u n s t a b l e Elow p a s t s l o t s . P r o c ASCE, J n l lIydr D i v ,

Vol 104 , HY5, May, pp 649-666.

Ethembabaoglu S (1979) . Some c h a r a c t e r i s t i c s of

s t a t i c p r e s s u r e s i n t h e v i c i n i t y of s l o t s . 1 3 t h ICOLD

Congress , New D e l h i , Vol 111, Q50, R20, pp 355-367.

Falvey H T (1979). Mean air concentration of

self-aerated flows. Proc ASCE, Jnl Hydr Div, Vol 105,

HY1, January, pp 91-96.

Falvey H T (1980). Air-water flow in hydraulic

structures. US Dept of Interior, Water and Power

Resources Service, Engng Monograph No 41.

Falvey H T (1982). Predicting cavitation in tunnel

spillways. Water Power 6 Dam Construction, Vol 34,

August. pp 13-15.

Falvey H T (1983). Prevention of cavitation on chutes

and spillways. Proc Conf on Frontiers in Hydraulic

Engineering, ASCE, Cambridge, USA, pp 432-437.

Falvey H T (1984). Cavitation studies in tunnel

spillways. Symp on Scale Effects in Modelling

Hydraulic Structures, IAHR/DVWK, Esslingen, FR

Germany, September, Paper 5.7

Galperin R et a1 (1971). Hydraulic structures

operation under cavitation conditions. Proc XIVth

IAHR Congress, Paris, Vol 5, pp 45-48.

Galperin R S et a1 (1977). Cavitation in Hydraulic

Structures. Energiya Publishing House, Moscow (in

Russian).

Gangadhariah T et a1 (1970). Inception and

entrainment in self-aerated flows. Proc ASCE, Jnl

Hydr Div, Vol 96, HY7, July, pp 1549-1565.

Haindl K (1984). Aeration at hydraulic structures.

Ch 3 in Developments in Hydraulic Engineering - 2, ed

P Novak, Elsevier Appl Sci Publ, London, pp 113-158.

Halbronn G (1951). Mesure des concentrations et des

vitesses dans un courant mixte d'air et d'eau. La

Houille Hlanche, Num6ro 3, pp 394-405.

Hamilton W S (1983). Preventing cavitation damage to

hydraulic structures. Water Power & Dam Construction,

Vol 35, (Part 1) November, pp 40-43; (Part 2)

December, pp 48-53.

Hamilton W S (1984). Preventing cavitation damage to

hydraulic structures. Water Power & Dam Construction,

Vol 36. (Part 3) January, pp 42-45.

Hammitt F G (1975a). Cavitation damage scale effects

- state of art summarization. Jnl Hydr Res, Vol 13,

No 1, pp 1-17.

Hammitt F G (1975b). Effects of gas content upon

cavitation, inception, performance and damage. Report

for Working Group No 1 for Hydraulic machinery,

equipment and cavitation. XIVth IAHR Congress,

Paris.

Harshbarger E D et a1 (1977). Discussion of "Air

entrainment in high head gated conduits" by

H R Sharma. Proc ASCE, Jnl Hydr Div, Vol 103, HY12,

December, pp 1486-1489.

Hart E D (1982). Air demand tests at Montana's Libby

Dam. Water Power h Dam Construction, Vol 34, July,

pp 19-22.

Hay N & White P R S (1975). Effects of air

entrainment on the performance of stilling basins.

Proc XVIth IAHR Congress, Sao Paulo, Vol 2,

pp363-372.

Hobbs J M (1967). Hydraulic cavitation erosion of

plastics. 2nd Cavitation Forum. ASME, Chicago,

pp 4-5.

Hsu H & Zhao Z (1982). Pressure distribution along

twcrdimensional circular and elliptic conduit inlets.

Collected Research Papers, IWHR, Beijing, Vol VII,

pp 84-97 (in Chinese).

Huang J et a1 (1985). The effect of air entrainment

on collapsing pressure of a cavitation bubble in a

liquid. Jnl Hydr Engng (Beijing), No 4, pp 10-17 (in

Chinese).

ICOLD (1980). Hydraulics for Dams. Draft report of

Committee on Hydraulics for Dams, ComitE Franqais des

Grands Barrages, Paris.

ICOLD (1986). Draft Bulletin on Design of Spillways

for Dams, Ch 5 "Particular problems with high-velocity

flows". Committee on Hydraulics for Dams.

Inozemtsev Y P et a1 (1965). Cavitational-erosion

resistance of hydrotechnical concretes on cement and

polymer binders. Proc XIth IAHR Congress, Leningrad,

Vol 1, Paper 48.

Iuditski G A (1965). Erosion par cavitation des

dissipateurs d'energie des barrages - deversoirs et les mesures de son elimination. Proc XIth IAHR

Congress, Leningrad, Vol 1, Paper 8.

Jiang F & Chen J (1982). Experimental study on

cavitation erosion resistance of concrete. Collected

Research Papers, IWHR, Beijing, Vol VII, pp 40-52 (in

Chinese).

Jin G (1983). Cavity characteristics of some baffle

piers located in the front part of a hydraulic jump.

Collected Research Papers, IWHR, Beijing, Vol XIII,

pp 237-254 (in Chinese).

Jin T et a1 (1980). Cavitation inception of gate

slots. Dept of Hydraulics, IWHR, Beijing.

Johnson V E (1963). Mechanics of cavitation. Proc

ASCE, Jnl Hydr Div, Vol 89, HY3, May, Part 1,

pp 251-275.

Kalinske A A h Robertson J W (1943). Entrainment of

air in flowing water - closed conduit flow. Trans

ASCE, Vol 108, pp 1435-1447.

Keller A (1972). The influence of the cavitation

nucleus spectrum on cavitation inception, investigated

with a scattered light counting method. Trans ASME.

Jnl Basic Engng, Vol 95, D4, December, pp 917-925.

Keller A P (1984). Scale effects at beginning

cavitation applied to submerged bodies. Symp on Scale

Effects in Modelling Hydraulic Structures. IAHR/DVWK,

Esslingen, FR Germany, September, Paper 1.14.

Keller A h Koch H-J (1982). Kavitationseinsatz an

umstromten quadratischen Schwellen in einem

Rechteckgerinne bei uberkritischen Fliesszustand.

Versuchsanstalt fur Wasserbau, Technical Univ of

Munich, May.

Keller R J h Rastogi A (1977). Design chart for

predicting critical point on spillways. Proc ASCE,

Jnl Hydr Div, Vol 103, HY12, December, pp 1417-1429.

Kenn M J (1968). Factors influencing the erosion of

concrete by cavitation. CIRIA, Technical Note 1.

Kenn M J (1971). Protection of concrete from

cavitation damage. Proc ICE, Vol 49, May, pp 75-79.

Kenn M J 6 Garrod A D (1981). Cavitation damage and

the Tarbela Tunnel collapse of 1974. Proc ICE,

Part 1, Vol 70, February, pp 65-89.

Knapp R T (1952). Cavitation mechanics and its

relation to the design of hydraulic equipment. Proc

Inst Mech Engrs, A, Vol 166, pp 150-163.

Knapp R T et a1 (1970). Cavitation. McGraw-Hill Book

CO, New York.

Koschitzky H-P et a1 (1984). Effects of model

configuration, flow conditions and scale in modelling

spillway aeration grooves. Symp on Scale Effects in

Modelling Hydraulic Structures, IAHRIDVWK, Esslingen.

FR Germany, September, Paper 4.4.

Kudriashov G V et a1 (1983). Cavitation and

cavitational erosion of members of water outlet

structures. Proc XXth IAHR Congress, Moscow, Vol 3,

pp 453-461.

Lakshmana Rao N S et a1 (1970). Characteristics of

self-aerated flows. Proc ASCE, Jnl Hydr Div, Vol 96,

HY2, February, pp 331-355.

Lakshmana Rao N S 6 Gangadhariah T (1971).

Self-aerated flow characteristics in wall region.

Proc ASCE, Jnl Hydr Div, Vol 97, HY9, September,

pp 1285-1303.

Lakshmana Rao N S 6 Kobus H E. Characteristics of

self-aerated free-surface flows. Water and Waste

Water: Current research and practice, Vol 10, Erich

Schmidt Verlag.

Lesleighter E J (1983). Cavitation in high-head gated

outlets - prototype measurements and model simulation. Proc XXth IAHR Congress, Moscow, Vol 3, pp 495-503.

Levin L (1965). Calcul hydraulique des conduits

d1a6ration des vidanges de fond et dispositifs

dcversants. La Houille Blanche, No 2, pp 121-126.

Li Z (1982). A study on spillway profiles with large

head drop. Jnl Hydr Engng (Beijing), No 9, pp 1-10

(in Chinese).

Li Z h Huang J (1985). Relation between cavitation

resistance of metals and their ultimate resilience.

Jnl Hydr Engng (Beijing), No 4, pp 60-66 (in

Chinese).

Lin B et a1 (1987). Hydraulic research in China.

Proc ASCE, Jnl Hydr Engng, Vol 113, No 1, January,

pp 47-60.

Liu C (1983). A study on cavitation inception of

isolated surface irregularities. Collected Research

Papers, IWHR, Beijing, Vol XIII, pp 36-56 (in

Chinese) .

Liu Y (1983). Cavitation in sediment laden flow. Jnl

Hydr Engng (Beijing), No 3, pp 55-58 (in Chinese).

Liu Y (1984). Scale effect on cavitation in

modelling. Symp on Scale Effects in Modelling

Hydraulic Structures, IAHR/DVWK, Esslingen. FR

Germany, September, Paper 1.13.

Locher F A h Hsu S T (1984). Energy dissipation at

high dams. Ch 5 in Developments in Hydraulic

Engineering-2, ed P Novak, Elsevier Appl Sci Publ,

London, pp 183-238.

Lopardo R A e t a 1 (1982). P h y s i c a l model l ing on

c a v i t a t i o n tendency f o r macro tu rbu lence of h y d r a u l i c

jump. I n t e r n Conf on Hydrau l i c Model l ing of C i v i l

E n g i n e e r i n g S t r u c t u r e s , BHRA, Coventry , pp 109-121.

Lopardo R A e t a 1 (1984). Model-prototype compar isons

on p r e s s u r e f l u c t u t i o n s i n h y d r a u l i c jump energy

d i s s i p a t o r s . Symp on S c a l e E f f e c t s i n Model l ing

H y d r a u l i c S t r u c t u r e s , IAHRIDVWK, E s s l i n g e n , FR

Germany, September , Paper 7.2

Lopardo R A e t a 1 (1985) . Model l ing t h e behaviour of

h i g h head h y d r a u l i c jump energy d i s s i p a t o r s under

f l o o d c o n d i t i o n s . 2nd I n t e r n Conf on H y d r a u l i c s of

F loods and Flood C o n t r o l , BHRA, Cambridge, England,

pp 313-324.

Low H S (1986) . Model s t u d i e s of Clyde Dam s p i l l w a y

a e r a t o r s . Dept C i v i l Engng, Research Repor t 86-6,

Univ of Can te rbury , New Zealand, March.

Lowe J e t a 1 (1979). Some e x p e r i e n c e s w i t h h i g h

v e l o c i t y f low a t T a r b e l a Dam p r o j e c t . 1 3 t h ICOLD

Congress , New D e l h i , Vol 111, Q50, R13, pp 215-247.

Lysne D K h Guttormsen 0 (1971). A i r demand i n h i g h

head r e g u l a t e d o u t l e t works. Proc XIVth IAHR

Congress , P a r i s , Vol 5, pp 77-80.

McGee R G (1984). P r o t o t y p e e v a l u a t i o n of s l u i c e w a y

a e r a t i o n system: Libby dam, Kootenai R i v e r , Montana.

US Army Engineer Waterways Experiment S t a t i o n , Tech

Repor t HL-84-2.

McKeogh E J e t a 1 (1983). V e l o c i t y and t u r b u l e n c e

measurements i n a i r / w a t e r f lows u s i n g l a s e r d o p p l e r

anemometry. Proc XXth I A H R Congress , Moscow, Vol 3 ,

pp 264-270.

Marcano A h Castillejo N (1984). Model-prototype

comparison of aeration devices of Guri dam spillway.

Symp on Scale Effects in Modelling Hydraulic

Structures, IAHRfDVWK, Esslingen, FR Germany,

September, Paper 4.6.

Mohammad W A h Hutton S P (1986). Improved monitoring

of air in water. Water Power h Dam Construction, Vol

38, September, pp 48-52.

Montero L A et a1 (1986). Desague de fondo de la

presa Colbun diseno, experimentacion en modelo y

seguimento de su operacion. Proc XIIth IAHR

Latin-American Congress on Hydraulics, Sao Paulo,

August.

Mousson J M (1937). Pitting resistance of metals

under cavitation conditions. Trans ASME, Vol 59,

pp 399-408.

Hurray M A h Schultheis V F (1977). Polymerization of

concrete fights cavitation. Civil Engineering (ASCE),

April, pp 67-70.

Narayanan R (1980). Cavitation induced by turbulence

in stilling basin. Proc ASCE, Jnl Hydr Div, HY4,

April, pp 616-619.

Naudascher E h Locher F A (1974). Flow-induced forces

on protruding walls. Proc ASCE, Jnl Hydr Div,

February, pp 295-313.

Novikova I S h Semenkov V M (1985). Permissible

irregularities on spillway structures surfaces based

on the conditions of cavitation erosion absence. Proc

of conferences and meetings on hydraulic engineering,

issue on "Hethods of investigations and hydraulic

analyses of spillway hydrotechnical structures",

Energoatomizdat, Leningrad, pp 170-174 (in Russian).

Oskolkov A G & Semenkov V M (1979). Experience in

designing and maintenance of spillway structures on

large rivers in the USSR, 13th ICOLD Congress, New

Delhi, Vol 111, Q50, R46, pp 789-802.

Ouazar D & Lejeune A (1984). Theoretical and

experimental study of cavitation prevention by

ventilation. Symp on Scale Effects in Modelling

Hydraulic Structures, IAHR/DVWK. Esslingen, FR

Germany, September, Paper 4.12

Pan S-B et a1 (1980). The self-aeration capacity of

the water jet over the aeration ramp. Jnl Hydr Engng

(Beijing), No 5.pp 13-22 (in Chinese).

Pan S & Shao Y (1984). Scale effects in modelling air

demand by a ramp slot. Symp on Scale Effects in

Modelling Hydraulic Structures, IAHR/DVWK. Esslingen,

FR Germany, September, Paper 4.7.

Pan S h Shao Y (1986). Hydraulic estimation of a

U-shape abrupt offset aeration device. Jnl Hydr Engng

(Beijing), No 8, pp 12-20 (in Chinese).

Peterka A J (1953). The effect of entrained air on

cavitation pitting. IAHRJASCE Minnesota Intern

Hydraulics Convention, Minneapolis, pp 507-518.

- - Pinto N L de S (1979). Cavitaqao aerafao em fluxos de

alta velocidade. CEPHAR, Curitiba, Brazil, -

Publica~ao, No 35.

Pinto N L de S (1984). Model evaluation of aerators

in shooting flow. Symp on Scale Effects in Modelling

Hydraulic Structures, IAHRIDVWK, Esslingen, FR

Germany, September, Paper 4.2.

Pinto N L de S (1986). Bulking effects and air

entraining mechanism in artificially aerated spillway

flow. Estudios in Honor de Francisco Javier Dominguez

Solar, Anales de la Universidad de Chile.

Pinto N L de S et a1 (1982). Aeration at high

velocity flows. Water Power S Dam Construction,

Vol 34, (Part 1) February, pp 34-38; (Part 2) March,

pp 42-44.

Pinto N L de S S Neidert S H (1982). Model-prototype

conformity in aerated spillway flow. Intern Conf on

Hydraulic Modelling of Civil Engineering Structures,

BHRA, Coventry, pp 273-284.

Pinto N L de S S Neidert S H (1983a). Evaluating

entrained air flow through aerators. Water Power 6

Dam Construction, Vol 35, August, pp 40-42.

Pinto N L de S 6 Neidert S H (1983b). Air entrainment

through aerators - mechanism and air flow evaluation. Proc XXth IAHR Congress, Moscow, Vol 7, pp 366-369.

Preece C M S Hansson I L H (1983). Cavitation erosion

of dense silica-cement mortar. Proc 6th Intern Conf

on Erosion by Liquid and Solid Impact, Cambridge,

England, Paper 3.

Prusza V et a1 (1983). Remedial measures against

spillway cavitation. Proc XXth IAHR Congress, Moscow,

Vol 3, 468-476.

Quintela A C et a1 (1979). L'gvacuateur de crue et

les vidanges de fond du barrage de M'Jara. 13th ICOLD

Congress, New Delhi, Vol 111, Q50, R40, pp691-711.

Quintela A C (1980). Flow aeration to prevent

cavitation erosion. Water Power 6 Dam Construction,

Vol 32, January, pp 17-22.

- Quintela A C h Ramos C M (1980). Protec~ao contra a

erosao de cavita$ao em obras hidraulicas. Laboratorio

Nacional de Engenharia Civil, Lisbon. Memoria No 539.

Rabben S L (1984). Untersuchung der Beluftung an

Tiefschiitzen unter besonderer Berucksichtigung von

Maktabseffekten. Mitteilungen 53, Institut fiir

Wasserbau und Wasserwirtschaft, Rheinisch-Westf'dlische

Technische Hochscule. Aachen.

Rabben St L et a1 (1983). Investigation of flow

aeration at offsets downstream of high-head control

structures. Proc XXth IAHR Congress, Moscow, Vol 7,

pp 354-360.

Rabben L 6 Rouv6 G (1984). Air demnd of high-head

gates - model-family studies to quantify scale effects. Symp on Scale Effects in Modelling Hydraulic

Structures, IAHRIDVWK, Esslingen, FR Germany,

September, Paper 4.9.

Regan R P et a1 (1979). Cavitation and erosion damage

of sluices and stilling basins at two high-head dams.

13th ICOLD Congress, New Delhi, Vol 111, Q50, R11,

pp 177-198.

Ripken J F h Hayakawa N (1972). Cavitation in

high-head conduit control dissipators. Proc ASCE, Jnl

Hydr Div, Vol 98, HY1, January, pp 239-256.

Robertson J M (1963). Cavitation in hydraulic

structures: scale effects in cavitation experiments.

Proc ASCE, Jnl Hydr Div, Vol 89, HY3, May, Part 1, pp

167-180.

Rosanov N P et a1 (1965). Research of vacuum and

cavitation characteristics of hydrotechnical

structures. Proc XIth IAHR Congress, Leningrad,

Vol 1, Paper 33.

Rouse H C Jezdinsky V (1965). Cavitation and energy

dissipation in conduit expansions. Proc XIth IAHR

Congress, Leningrad, Vol 1, Paper 28.

Rouse H h Jezdinsky V (1966). Fluctuation of pressure

in conduit expansions. Proc ASCE, Jnl Hydr Div, Vol

92, HY3, May, pp 1-12.

Rozanov N P et a1 (1971). Cavitation tests on baffle

piers and bucket splitters of spillway hydraulic

structures. Proc XIVth IAHR Congress, Paris, Vol 5,

pp 57-60.

Rozanov N P h Rozanova N N (1981). Some problems of

modelling water outlet structures with free-surface

flow. Proc XIXth IAHR Congress, New Delhi, Vol 5,

pp 81-91.

Rozanova N N h Ariel A R (1983). Cavitation and

hydraulic studies of non-erodible energy dissipators.

Proc XXth IAHR Congress, Moscow, Vol 7, pp 400-405.

Russell S 0 h Ball J W (1967). Sudden enlargement

energy dissipator for Mica Dam. Proc ASCE, Jnl Hydr

Div, Vol 93, HY4, July, pp 41-56.

Russell S 0 h Sheehan G J (1974). Effect of entrained

air on cavitation damage. Canadian Jnl Civil Engng,

v01 1.

Sakhuja V S et a1 (1984). Air entrainment distortion

in free surface flows. Symp on Scale Effects in

Modelling Hydraulic Structures, IAHR/DVWK, Esslingen,

FR Germany, September, Paper 4.8.

Scheur L (1985). Theoretische und experimentelle

Untersuchungen zum Kavitationsbeginn an

Oberflachenrauheiten. Mittellungen 57, Institut fur

Wasserbau und Wasserwirtschaft, Rheinisch-Westfslische

Technische Hochscule, Aachen.

Schmitt R W (1971). Cavitation damage at Kinzua Dam,

Allegheny Reservoir. Proc XIVth IAHR Congress, Paris,

Vol 5, pp 97-101.

Schrader E K (1983). Cavitation resistance of

concrete structures. Proc Conf on Frontiers in

Hydraulic Engineering, ASCE, Cambridge, USA,

pp 419-424.

Schrader E K h Munch A V (1976). Fibrous concrete

repair of cavitation damage. Proc ASCE, Jnl Constr

Div, C02, June, pp 385-399.

Schwarz H I h Nutt L P (1963). Projected nappes

subject to transverse pressure. Proc ASCE, Jnl Hydr

Div, Vol 89, HY4, July, Part 1, pp 97-104.

Semenkov V S h Lentjaev L D (1973). Spillway dams

with aeration of flow over spillways. 9th ICOLD

Congress, Madrid, Separate Paper.

Sharma H R (1976). Air entrainment in high head gated

conduits. Proc ASCE, Jnl Hydr Div, Vol 102, HY11,

November, pp 1629-1646.

Sharma H R h Goel R S (1983). Cavitation problems in

outlet structures. Proc XXth IAHR Congress, Moscow,

Vol 3, pp 504-512.

Shengzhong X (1984). A cavitation-free form of

lift-gate slots operated under high pressure. 4th

IAHR Congress, Asian h Pacific Division, Chiang Mai,

Thailand, pp 581-591.

Shi Q et a1 (1983). Experimental investigation of

flow aeration to prevent cavitation erosion by a

deflector. Jnl Hydr Engng (Beijing), No 3, pp 1-13

(in Chinese).

Stebbins R J (1978). Polymer-impregnated concrete at

Dworshak dam. Proc ASCE, Jnl Constr Div, C04,

December, pp 539-547.

Straub L G h Anderson A G (1958). Experiments on

self-aerated flow in open channels. Proc ASCE, Jnl

Hydr Div, Vol 84, HY7, December, Part 1,

pp 189011-35.

Tabor L J (1978). Effective use of epoxy and

polyester resins in civil engineering structures.

CIRIA Report 69.

Tan T P (1984). Model studies of aerators on

spillways. Dept of Civil Engng, Research Report 84-6,

Univ of Canterbury, New Zealand, February.

Thandaveswara B S h Lakshmana Rao N S (1978).

Developing zone characteristics in aerated flows.

Proc ASCE, Jnl Hydr Div, Vol 104, HY3, March,

pp 385-396.

Thiruvengadam A (1960). Discussion of "Cavitation

damage of roughened concrete surfaces" by D Colegate,

Proc ASCE, Jnl Hydr Div, Vol 86, HY4, April,

pp 127-129.

Tomita Y h Shima A (1986). Mechanisms of impulsive

pressure generation and damage pit formation by bubble

collapse. Jnl Fluid Mech, Vol 169, pp 535-564.

Tullis J P (1981). Modelling cavitation for closed

conduit flow. Proc ASCE, Jnl Hydr Div, Vol 107, HYll,

November, pp 1335-1349.

Tullis J P h Govindarajan R (1973). Cavitation and

size scale effects for orifices. Proc ASCE, Jnl Hydr

Div, Vol 99, HY3, March, pp 417-430.

US Army Corps of Engineers (1964). Hydraulic design

criteria: Air demand-regulated outlet works.

Uppal H L et a1 (1965). Cavitation in high-head

outlet conduits. Proc XIth IAHR Congress, Leningrad,

Vol 1, Paper 1.30.

Vernet G F h Larrea J C (1985). Prototype and model

aeration efficiency in a high head outlet for flood

flows. 2nd Intern Conf on Hydraulics of Floods 6

Flood Control, BHRA, Cambridge, England, pp 365-372.

Vinnogg L (1971). Cavitation with high-head leaf

gates. Proc XIVth IAHR Congress, Paris, Vol 5,

pp 81-86.

Vischer D et a1 (1982). Hydraulic modelling of air

slots in open chute spillways. Intern Conf on

Hydraulic Modelling of Civil Engineering Structures,

BHRA, Coventry, pp 239-252.

Volkart P U (1982). Self-aerated flow in steep,

partially filled pipes. Proc ASCE, Jnl Hydr Div, Vol

108, HY9, September, pp 1029-1046.

Volkart P 6 Chervet A (1983). Air slots for flow

aeration: Determination of shape, size and spacing of

air slots for the San Roque Dam Spillway.

Mitteilungen der Versuchsanstalt fur Wasserbau,

Hydrologie und Glaziologie, ETH, Zurich. Nr 66.

Volkart P 6 Rutschmann P (1984a). Air entrainment

devices (Air slots). Mitteilungen der Versuchsanstalt

fur Wasserbau, Hydrologie und Glaziologie, ETH,

Zurich, Nr 72.

Volkart P 6 Rutschmann P (1984b). Rapid flow in

spillway chutes with and without deflectors - a model-prototype comparison. Symp on Scale Effects in

Modelling Hydraulic Structures, IAHR/DvWK, Esslingen,

FR Germany, September, Paper 4.5.

Vorobiyov G A (1983). Methods of cavitational erosion

consideration when designing hydraulic structures.

Proc XXth IAHR Congress, Moscow, Vol 7, pp 394-397.

Wagner W E (1967). Glen Canyon Dam diversion tunnel

outlets. Proc ASCE, Jnl Hydr Div, Vol 93, HY6,

November, pp 113-135.

Wagner W E 6 Jabara M A (1971). Cavitation damage

downstream from outlet works gates. Proc XIVth IAHR

Congress, Paris, Vol 5, pp 93-96.

Wang J-Y (1981). Comparison of depth formulae for

high velocity aerated channel flow. Jnl Hydr Engng

(Beijing), No 5, pp 48-52 (in Chinese).

Wang S (1984). A formula for estimating air

concentration of self-aerated flow in open channels.

Jnl Hydr Engng (Beijing), No 7, pp 44-49 (in

Chinese).

Wang X-R & Chou L-T (1979). The method of calculation

of controlling (or treatment) criteria for the

spillway surface irregularities. 13th ICOLD Congress,

New Delhi, Vol 111, Q50. R56, pp 977-1012.

Warner J (1980). Epoxies - "miracle" materials don't always give miracle results. Civil Engineering

(ASCE), February, pp 48-55.

Wei C Y & De Fazio F G (1982). Simulation of free jet

trajectories for the design of aeration devices on

hydraulic structures. 4th Intern Conf on Finite

Elements in Water Resources, DFG/ISCME/IAHR, Hannover,

pp 17/45-54.

White P R S 6 Hay N (1975). A portable air

concentration meter. Proc XVIth IAHR Congress, S ~ O

Paulo, Vol 3, pp 541-548.

Wisner P (1965). Sur le r61e du critPre de Froude

dans lt6tude de l'entrainment de l'air par les

courants Bgrande vitesse. Proc XIth IAHR Congress,

Leningrad, Vol 1, Paper 1.15.

Wood I R (1983). Uniform region of self-aerated flow.

Proc ASCE, Jnl Hydr Engng, Vol 109, No 3, March,

pp 447-461.

Wood I R (1985). Air water flows. Proc XXIst IAHR

Congress, Melbourne, Vol 6, pp 18-29.

Wood I R et a1 (1983). General method for critical

point on spillways. Proc ASCE, Jnl Hydr Engng,

Vol 109, No 2, February, pp 308-312.

Xu X 6 Zhou S (1982). Pressure distribution and

incipient cavitation number for isolated irregularity

formed w i t h a c i r c u l a r a r c . C o l l e c t e d Research

P a p e r s , IWHR, B e i j i n g , Vol V I I , pp 1-13 ( i n Chinese ) .

Yan Z e t a 1 (1982). The model s t u d y on t h e c a v i t y

f low of a s p i l l w a y o u t l e t . C o l l e c t e d Research P a p e r s ,

IWHR, B e i j i n g , Vol V I I , pp 14-39 ( i n Chinese ) .

Yen C L e t a 1 (1984). Flow c h a r a c t e r i s t i c s around a n

a e r a t i o n d e v i c e i n t u n n e l s p i l l w a y . Proc 4 t h IAHR

Congress. Asian h P a c i f i c D i v i s i o n , Chiang Mai,

T h a i l a n d , pp 669-684.

Yue Y (1984). H y d r a u l i c c h a r a c t e r i s t i c s of f l o w

p a t t e r n and c a v i t a t i o n i n g a t e s l o t s . C o l l e c t e d

Research P a p e r s , IWHR, B e i j i n g , Vol X X I , pp 295-298

( i n Chinese ) .

Yung K h Pataky T (1986) . C a v i t a t i o n i n h y d r a u l i c

s t r u c t u r e s i n B r i t i s h Columbia. ( P e r s o n a l

communication).

Z a g u s t i n K e t a 1 (1982) . Some e x p e r i e n c e on t h e

r e l a t i o n s h i p between a model and p r o t o t y p e f o r f low

a e r a t i o n i n s p i l l w a y s . I n t e r n Conf on H y d r a u l i c

Model l ing of C i v i l Eng ineer ing S t r u c t u r e s , BHRA,

Coventry , pp 285-295.

Z a g u s t i n K h C a s t i l l e j o N (1983) . Model-prototype

c o r r e l a t i o n f o r f low a e r a t i o n i n t h e Guri-Dam

s p i l l w a y . Institute de Mecanica d e F l u i d o s ,

U n i v e r s i d a d C e n t r a l de Venezuela , F a c u l t a d d e

I n g e n i e r i a , B o l e t i n No 6.

Zhang S (1984) . Labora to ry s t u d y of c a v i t a t i o n

problems and s u r f a c e i r r e g u l a r i t y c o n t r o l of t h e

i n v e r t i n s t e e p open channe l . H y d r a u l i c s Lab, Royal

I n s t i t u t e of Technology, Stockholm, B u l l e t i n

TRITA-VBI-127.

Zharov N I & Kudryashov G V (1977). Caviration in

flow around three-dimensional projections on spillway

surfaces. Fluid Mechanics-Soviet Research, Vol 6, No

3, May-June, pp 118-125.

Zheng D (1984). Investigation of the resistance

against cavitation damage of bitumen mortar.

Collected Research Papers, IWHR, Beijing, Vol XXI,

pp 254-258 (in Chinese).

Zhou S et a1 (1984). Pressure distribution and

incipient cavitation number for surface irregularities

with rounded corners in a pressure conduit. Jnl Hydr

Engng (Beijing), No 6, pp 36-45 (in Chinese).

Zhu R (1984). Some hydraulic problems of aerator with

step and lateral offsets. Collected Research Papers,

IWHR, Beijing, Vol XXI, pp 40-51 (in Chinese).

Zhu X et a1 (1982). Pressure distribution in square

and rectangular entrances to conduits. Collected

Research Papers, IWHR, Beijing, Vol VII, pp 98-122 (in

Chinese).

Zhuravliova A G (1983). Conditions of cavitation

inception on smoothly-undulate surfaces of spillways.

Proc XXth IAHR Congress, Moscow, Vol 7, pp 406-409.